2,739 results
Search Results
2. A mathematical review on Caputo fractional derivative models for Covid-19.
- Author
-
Suganya, S. and Parthiban, V.
- Subjects
CAPUTO fractional derivatives ,SARS-CoV-2 ,COVID-19 ,DIFFERENTIAL equations ,SCIENTIFIC community - Abstract
Several papers on the dynamics and early identification of COVID-19 by mathematical modelling have been published in the last two years. This review will look at the quantitative analysis and dynamical behaviors of novel coronavirus, with a focus on the Caputo fractional derivative. Currently many mathematical models are used to investigate the Novel coronavirus under Caputo fractional order system of differential equations. In this paper, we have focused on reviewing the Caputo fractional model of Covid 19, local stability and optimal control. The purpose of this work is to provide the research community a complete overview of the Caputo fractional derivative approach used in these investigations. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
3. On Generalized Vieta-Pell functions and their associated operational matrices.
- Author
-
Khaleel, Inas Abd Ulkader and Shihab, Suha
- Subjects
VECTOR valued functions ,DIFFERENTIAL equations - Abstract
This paper studies the properties of Generalized Vieta Pell Functions (GVPFs). Then new definition for such functions is considered with some interesting properties. The definite expression for constructing the operation matrix of the derivative of GVPFs is given, which is the direct method to find the higher-order derivative according to the requirement of the total differential equation. The explicit expression that relates the power function with the GVPFs is formulated in this work. Another contribution of the present paper is the generation of words for the product of two Generalized Vieta Pell Function vectors. All the results mentioned above are applicable in a wide range of computational processes and useful for finding more exact results. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
4. Advanced color image encryption using third-order differential equations and three-dimensional logistic map.
- Author
-
Abdul-Hameed, M., El-Metwally, H., Askar, S., Alshamrani, A. M., Abouhawwash, M., and Karawia, A. A.
- Subjects
ORDINARY differential equations ,DIFFERENTIAL equations ,CONSTANTS of integration ,INDEPENDENT variables ,THREE-dimensional imaging ,IMAGE encryption - Abstract
Image encryption stands out as a crucial technique employed to securely transmit images across the Internet. In this paper, we introduce a novel algorithm for encrypting color images. The algorithm is built upon the principles of differential equations, XOR operations, and chaotic maps. First, the plain image is three-dimensional pixel shuffled via a logistic map. Afterward, the differential equations are used as a mathematical tool for encrypting images. The third-order ordinary differential equations are used to encrypt the shuffled images. The color values of the plain image are considered coefficients for the independent variable X. Subsequently, an alternate matrix of the same size is generated using a three-dimensional logistic map, taking into account its color values as the exponents linked to the independent variable X. A set of third-order differential equations emerged, containing an equivalent number of elements as the color values present in the plain image. This set of differential equations is addressed in the following manner: combining XOR and integration three times with respect to the independent variable X for each set of obtained differential equations while treating the integration constant as zero. Ultimately, a set of ordinary equations involving the independent variable X is derived, where the coefficients of X represent color values for the cipher image. The results from experiments and the security analysis affirm the resilience of the proposed algorithm against established security attacks. It exhibits a substantial key space, heightened key sensitivity, and a strong encryption effect. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
5. A numerical study for solving higher-order fuzzy differential equations using modified RKM methods.
- Author
-
Mechee, Mohammed S., Salman, Zahrah I., and Al Shuwaili, Basim K.
- Subjects
DIFFERENTIAL equations ,ORDINARY differential equations - Abstract
In this paper, direct explicit numerical RKM methods for solving classes of higher-order ordinary differential equations (ODEs) have been developed and modified to be appropriate with fuzzy differential equations (FDEs) with more computational efficiency. The aim of this paper is to derive the numerical methods of RKM type to solve some classes of higher-order FDEs. The numerical results of implementation showed that the efficiency and advantage of the proposed integrators comparing with classical RK methods in sense of evaluation computational time. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
6. Controllability of the nonlinear smoking model.
- Author
-
Tjahjana, R. H., Herdiana, R., and Permatasari, A. H.
- Subjects
- *
CONTROLLABILITY in systems engineering , *NONLINEAR differential equations , *NONLINEAR equations , *SMOKING , *DIFFERENTIAL equations - Abstract
This paper exposes the controllability problem of the nonlinear smoking model. Mathematically, the form of smoking model is the first order of nonlinear differential equation system. The model consists of six variables and two controls. The most important thing before controlling a smoker is to determine its controllability. If the smoking model is in nonlinear standard control model, then it has drift. Applying the Lie Bracket method, the controllability matrix can be found. After determining the rank of the controllability matrix, the controllability of the model can be determined. The result can be stated that the smoking model is locally accessible. This means the control design can be made to control the smoker. In addition, if the optimal control approach is used in controlling the smoking model, through its cost functional model, we can make minimization of beginners and smokers. Another result of this paper is the presentation of optimal control analysis using the Pontryagin Principle approach. The analysis results can be stated as follows, first, each solution of the equation in the dynamic system model is a positive function, second, the model of the system of differential equations with the given initial conditions, has a solution, and that solution is a single solution. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
7. Optimization of difference formulas for solving differential equations in the Hilbert space.
- Author
-
Shadimetov, Kholmat and Esanov, Shermamat
- Subjects
- *
DIFFERENTIAL equations , *NUMERICAL solutions to initial value problems , *NUMERICAL functions , *SOBOLEV spaces , *FUNCTION spaces , *ORDINARY differential equations - Abstract
In the numerical solution of Initial Value Problems (IVP) for ordinary differential equations, computational methods serve to approximate the determination of functions representing the solution of these problems. The problem of finding the most convenient numerical expressions for a function and its connection with methods for improving such approximations plays an important role in practical calculations. It is of great interest to consider the so-called discrete methods, i.e. methods that determine the solution for discrete values of the independent variable. Discrete methods are currently the most widely used. One of the discrete methods is difference formulas for the numerical solution of the IVP. In this paper, in the Sobolev space where all derivatives up to the mth order participate in the norms of functions, we consider the problem of constructing optimal difference formulas. In the optimization of difference formulas, i.e. when constructing optimal difference formulas in function spaces, an important role is played by the extremal function of a given difference formula. In this paper, the extremal function of the difference formula is explicitly found in the Sobolev space. Next, the square of the norm of the error functional of difference formulas is calculated. Minimizing this norm with respect to the coefficients of the difference formulas, a system of equations is obtained. In addition, the existence and uniqueness of a solution to the resulting system are proved. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
8. Study of stationary rigidly rotating anisotropic cylindrical fluids with new exact interior solutions of GR. IV. Radial pressure.
- Author
-
Célérier, M.-N.
- Subjects
MATHEMATICAL simplification ,ROTATING fluid ,DIFFERENTIAL equations ,FLUIDS ,EQUATIONS ,AZIMUTH - Abstract
This article belongs to a series where the influence of anisotropic pressure on gravitational properties of rigidly rotating fluids is studied using new exact solutions of GR constructed for the purpose. For mathematical simplification, stationarity and cylindrical symmetry implying three Killing vectors are considered. Moreover, two pressure components are set to vanish in turn. In Papers I and II, the pressure is axially directed, while it is azimuthal in Paper III. In present paper (Paper IV), a radially directed pressure is considered. Since a generic differential equation, split into three parts, emerges from field equations, three different classes of solutions can be considered. Two could only be partially integrated. The other one, which is fully integrated, yields a set of solutions with a negative pressure. Physical processes where a negative pressure is encountered are depicted and give a rather solid foundation to this class of solutions. Moreover, these fully integrated solutions satisfy the axisymmetry condition, while they do not verify the so-called "regularity condition." However, since their Kretschmann scalar does not diverge on the axis, this feature must be considered as reporting a mere coordinate singularity. Finally, the matching of these solutions to an exterior appropriate vacuum enforces other constraints on the two constant parameters defining each solution in the class. The results displayed here deserve to be interpreted in light of those depicted in the other four papers in the series. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
9. A priori selected spline–wavelet basis for option pricing under Black–Scholes and Merton model.
- Author
-
Černá, Dana
- Subjects
BLACK-Scholes model ,PRICES ,SPARSE matrices ,A priori ,DIFFERENTIAL equations ,SPLINES - Abstract
The paper deals with option pricing under the classical Black-Scholes model and a more sophisticated Merton jump– diffusion model, which allows jumps in the underlying asset price. The Merton model is represented by non–stationary integro– differential equations. Due to the integral term, standard methods are not very efficient because they lead to full discretization matrices. The Black–Scholes model can be considered a particular case of the Merton model, which does not contain the integral term. In the paper, a method is proposed, which is a combination of the Crank–Nicolson scheme and the wavelet–Galerkin method using adaptive quadratic spline wavelet basis selected a priori. This enables to significantly decrease the number of basis functions and size of matrices and vectors involved in computation compared to standard non–adaptive wavelet–Galerkin methods. Furthermore, the proposed wavelet–based method leads to sparse discretization matrices with uniformly bounded condition numbers. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
10. Compact Integrated Radial Basis Function (CIRBF) for natural convection flow in a square cavity.
- Author
-
Thai, Thinh Q. and Thai-Quang, Nha
- Subjects
RADIAL basis functions ,NATURAL heat convection ,NEWTONIAN fluids ,DIFFERENTIAL equations ,NAVIER-Stokes equations ,CRANK-nicolson method - Abstract
This paper presents a numerical scheme to approximate a set of differential equations establishing the behavior of Newtonian fluid motion. The three primary differential equations are the continuity equation, the momentum equation (aka the Navier-Stokes equation) and the energy equation. The paper uses a numerical approach namely Compact Integrated Radial Basis Function (CIRBF) to approximate space variables whereas Crank-Nicolson and Adams-Bashforth methods are adopted to discretize temporal variables. More specifically, the spatial approximation at a point is obtained by collecting the desired information of two adjacent nodes along with their corresponding derivatives. Our scheme is verified by comparison with the benchmark solution of natural convection flow in a square cavity. The solution is in good agreement with the previously published results, thereby showing the robustness and reliability of CIRBF approach. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
11. Third Symposium on “Recent Trends in the Numerical Solution of Differential Equations”: Preface.
- Author
-
Brugnano, Luigi and Weinmüller, Ewa
- Subjects
CONFERENCES & conventions ,NUMERICAL analysis ,DIFFERENTIAL equations ,EIGENVALUES ,RUNGE-Kutta formulas - Abstract
Information about the third symposium on Recent Trends in the Numerical Solution of Differential Equations is presented. Topics include numerical methods for eigenvalue problems and analysis of boundedness of general linear methods. In addition, the event highlighted various studies including the use of the well-known technique of defect correction and a new practical strategy to detect stiffness based on explicit Runge-Kutta schemes.
- Published
- 2010
- Full Text
- View/download PDF
12. Simulation of wave propagation with obstacles: Time invariance operator applied to interference and diffraction.
- Author
-
Oliveira, Marceliano, Rodrigues, Francisco, Valadares, George, and Freire, Márcio
- Subjects
THEORY of wave motion ,COMPUTATIONAL physics ,COMPUTATIONAL fluid dynamics ,EVOLUTION equations ,DIFFERENTIAL equations ,WAVE diffraction ,WAVE equation - Abstract
We present here a computational numerical operator, and we name it as Time Invariance Operator (TIO). This operator can add obstacles to the domain of the differential equation that describes a physical phenomenon. After the TIO acts, the wave equation recognizes the introduced points as non-interacting zones without affecting the rest of the domain. Computational physics has been consolidated as an important field of study, especially when connected with the fundamentals of physics. In many cases, simulations are conducted considering the ideal case of a wave in an infinite domain and open space without considering obstacles, barriers, or other aspects of the real world. The results presented in this paper allow us to infer that the TIO is the easiest way to apply the physical domain to wave propagation simulations and successfully recreate wave interaction experiments through computer simulations. Our motivation is to perform wave simulations that interact with obstacles, barriers, single slits, and double slits. We aim to investigate the results obtained in images to determine if the methodology we used to introduce realistic physical characteristics was successful in presenting the expected phenomenology. The simplicity of the TIO's action in creating locally time-invariant regions over the domain makes it suitable not only for waves but also for equations with transient terms. Heat transfer, mass transfer, computational fluid dynamics, and other time evolution equations can take some benefit from the operator presented in this paper. The TIO ensures local conservation that mimics interaction regions or ensures free space characteristics if it is the case like a 2D tensor of local conservation. The principal result from this paper is the validation of the TIO to impose realistic conditions with minimal modifications over a running code of wave equation simulation originally in free space. The TIO is innovative because it imposes dynamic conditions that mimic realistic interacting zones. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
13. Mathematical modeling of rigid diaphragm geometry in MEMS pressure sensor.
- Author
-
Nag, Meetu, Mehta, Ruchika, and Pratap, Bhanu
- Subjects
PRESSURE sensors ,MATHEMATICAL models ,DIFFERENTIAL equations ,GEOMETRY - Abstract
Silicon has remarkable mechanical properties, and it is a very promising material for MEMS pressure sensors. The Silicon diaphragm plays an important role in enhancing the sensitivity and linearity of the pressure sensor. In this paper, a silicon diaphragm is modeled by solving the analytical equations for both rigidly clamped and freely supported diaphragms by exploring the solution of differential equation and dependency on the different parameters of the diaphragm. For obtaining maximum deflection of the diaphragm, boundary conditions are applied for different loads. COMSOL Multiphysics is used to simulate the optimum geometry of the diaphragm for enhancing the sensitivity of the pressure sensor. Results reveal that diaphragm thickness of 20 µm shows the high displacement sensitivity of the pressure sensor. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
14. Application of Extended Kalman Filter in Antibiotic Resistance Research.
- Author
-
Anrui Fu, Bo Wang, and Minghong Yao
- Subjects
DRUG resistance in bacteria ,KALMAN filtering ,QUANTITATIVE research ,ANTIBIOTICS - Abstract
This article uses quantitative methods to put forward some solutions on antibiotic resistance crisis. In order to describe the propagation process of a bacterium, the paper selects the sales volume of antibiotics to reflect the changes in bacterial antibiotic resistance. On this basis, the article simulates the trend of bacterial resistance in a perfect competitive market. The result shows that the disease can repeat in the next several years and never fade away. From the result, the paper comes out a conclusion that it is essential to stop offering antibiotics duly in order to eradicate the bacteria. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
15. Static and free vibration responses of nanobeams considering flexoelectricity and surface effect.
- Author
-
Liu, Zhuorui and Zhou, Zhidong
- Subjects
FLEXOELECTRICITY ,STRAINS & stresses (Mechanics) ,ELECTRIC potential ,FREE vibration ,SURFACE potential ,RESIDUAL stresses ,DIFFERENTIAL equations - Abstract
In this paper, the electro-mechanical behavior of a flexoelectric nanobeam, considering the surface effect, is studied with an induced electric potential. Based on the modified strain gradient theory and Hamilton's variational principle, the governing differential equations of the nanobeam and the corresponding boundary conditions are obtained. The exact deflection solution of the flexoelectric nanobeam is derived from static bending. The relationship between the induced electric potential, including the surface effect, and the angle of the end of the cantilever beam is presented. Moreover, the characteristic equation of natural frequency is obtained by using a separate variable method under an open circuit with surface electrodes and an induced electric potential condition (OCI). The simulated results indicate the electro-mechanical response of the cantilever beam can be controlled by adjusting the flexoelectric coefficient, residual surface stress, and material length scale parameters of strain gradient theory. The free end of the beam with a platform phenomenon is also found by setting the appropriate parameters. The results also show that the residual surface stress and the ratio of beam thickness to material length scale parameters have a more significant effect on the effective frequency shift of the flexoelectric nanobeam. Therefore, considering the induced electric potential and surface effect is of great significance for the study of flexoelectric nanobeam sensors. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
16. Synchronization of differential equations driven by linear multiplicative fractional Brownian motion.
- Author
-
Wei, Wei, Gao, Hongjun, and Cao, Qiyong
- Subjects
LINEAR differential equations ,BROWNIAN motion ,STOCHASTIC differential equations ,RANDOM dynamical systems ,SYNCHRONIZATION ,DIFFERENTIAL equations - Abstract
This paper is devoted to the synchronization of stochastic differential equations driven by the linear multiplicative fractional Brownian motion with Hurst parameter H ∈ ( 1 2 , 1). We use equivalent transformations to prove that the differential equation has a unique stationary solution, which generates a random dynamical system. Moreover, the system has the pathwise singleton set random attractor. We then establish the synchronization of the coupled differential equations and provide numerical simulation results. At the end, we discuss two specific noise forms and present the corresponding synchronization results. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
17. Coupled coincidence best proximity point results for generalized Ciric contractions.
- Author
-
Hussain, Nawab, Asiri, Asim, Shafqat, Naeem, Hussain, Aftab, and Anees, Zubair
- Subjects
COINCIDENCE ,DIFFERENTIAL equations ,COINCIDENCE theory ,METRIC spaces ,POINT set theory ,GENERALIZATION - Abstract
In this paper, we define a generalized C ́ i r i c contraction with respect to ℸ and prove some coupled coincidence best proximity point results in the setting of complete metric spaces. We also obtain some coupled best proximity point results for such contractions. We provide an example for the validity of our main result. Our results are the generalization of many results existing in the literature. As an application, we find the solution of the differential equation. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
18. Spoon Design Using Partial Differential Equations.
- Author
-
Ismail, Nur Baini and Ahmat, Norhayati
- Subjects
SPOONS ,PARTIAL differential equations ,DIFFERENTIAL equations ,FINITE volume method ,CURVES - Abstract
Spoon is a form of free-form surfaces. In this paper, a method for designing a spoon using partial differential equations (PDE) is discussed. Boundary curves are defined in term of Fourier series. By selecting the appropriate boundary curves, a design of spoon is generated using fourth order elliptic PDE. Then by solving the elliptic PDE, a smooth design of spoon can be generated. In addition, this paper also examined the impact of the choice of number of boundary curves in generating different spoon shapes. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
19. Study the solutions of differential equations by Laplace transform: A review.
- Author
-
Singla, Garima and Nagar, Harish
- Subjects
- *
DIFFERENTIAL equations , *ALGEBRAIC equations , *LAPLACE transformation , *SIMULTANEOUS equations , *INTEGRAL equations , *RESEARCH personnel - Abstract
Laplace transform is a principal technique which is discover to find the solution of various problem in a real life. Laplace transform is one of the most efficient tools which is used by the researchers to identify the solutions of various real problems patterned into differential equations or simultaneous differential equations and integral equations which is easily solvable by Laplace method. In this paper, we are proceeding to study the details on Laplace transform, its properties and "study on solving differential equation by Laplace transform". Laplace transform bring to the ordinary differential equations into an algebraic sum. This paper represents how ordinary differential equations is solved through Laplace transform. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
20. Study review: The existence of strong and weak solutions to Banach spaces in mathematical differential equations.
- Author
-
Alfaris, Lulut, Siagian, Ruben Cornelius, Kaimuddin, Januar Saleh, and Sumarto, Eko Pramesti
- Subjects
- *
BANACH spaces , *DIFFERENTIAL equations , *NONLINEAR differential equations - Abstract
An investigation of the use of Banach spaces for finding solutions to non-linear differential equations is conducted in this paper, focusing on weak and strong solutions. We present 12 theorems and several mathematical assumptions to support the findings, which conclude that, under certain conditions, at least one weak solution for the non-linear differential Equation is obtained in Banach spaces. Furthermore, it is suggested in the paper that the same result can be obtained by expanding upon the compactness assumption. The properties of weak and strong solutions of non-linear differential equations using Banach spaces are improved upon by this research, and its potential real-world applications are highlighted. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
21. Weighted optimal order of convergence cubature formulas in Sobolev space L¯P(m) (Kn).
- Author
-
Jalolov, Ozodjon
- Subjects
CUBATURE formulas ,SOBOLEV spaces ,THEORY of distributions (Functional analysis) ,DIFFERENTIAL equations - Abstract
The main area of application of various spaces of generalized functions lies in the theory of differential equations and in the theory of quadrature and cubature formulas. Therefore, it becomes necessary to study spaces of generalized functions, one way or another related to various domains in R
n . The theory of differential equations in the space of generalized functions differs from the theory of these equations in the space of ordinary functions. Deriving these equations and finding their solutions are important in applications. In the study of various questions arising in the theory of approximate integration and partial differential equations and related departments of analysis, the so-called Functional approach turned out to very fruitful. In this paper we investigate weighted cubature formula in the functional spaces L ¯ P (m) of S.L. Sobolev for the functions defined in the n - dimensional unit cube Kn and obtain an upper estimate for the norm of error functionals of weighted cubature formulas. Based on the Bakhvalov theorem it is proved that considered cubature formulas of the optimal on order of convergence in these spaces. [ABSTRACT FROM AUTHOR]- Published
- 2023
- Full Text
- View/download PDF
22. Homotopy perturbation method for solution of q-fractional differential equations.
- Author
-
Madhavi, B., Kumar, G. Suresh, and Rao, T. Srinivasa
- Subjects
DIFFERENTIAL equations ,NONLINEAR differential equations ,FRACTIONAL differential equations ,TOPOLOGY - Abstract
In this paper, we present a numerical method for solving nonlinear q-fractional differential equations(q-FDEs). Here, we consider q-fractional derivative in the Caputo sense. The homotopy perturbation method(HPM) is applied to construct the numerical solutions. Using homotopy technique in topology, a homotopy is built with an installing parameter s ∈ (0, 1), and is treated as a small parameter. Numerical provide the applicability and validity of this method. The proposed method is consistently valid for small parameters as well as for large parameters. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
23. See transform and convolution theorem in fractional differential equations.
- Author
-
Patil, Dinkar P. and Khakale, Savita S.
- Subjects
FRACTIONAL differential equations ,DIFFERENTIAL equations ,MATHEMATICAL convolutions - Abstract
Now a day's integral transform play very important role in differential equations. In this paper we apply SEE Transform Method and prove convolution theorem to solve linear homogeneous and non-homogeneous Fractional Differential Equations with constant coefficients. The Caputo sense used to describe fractional derivatives. The validity and applicability of the presented technique is verified by including some examples. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
24. Low-Thrust multi-revolutionary trajectories to geostationary orbit using angular independent variable.
- Author
-
Oo, Paing Soe Thu
- Subjects
ORBITS (Astronomy) ,BOUNDARY value problems ,TRAJECTORY optimization ,DIFFERENTIAL equations ,CONTINUATION methods ,INDEPENDENT variables ,MAXIMUM principles (Mathematics) - Abstract
In this paper, the problem of optimization of multi-revolutionary transfers of a spacecraft with a fixed angular range of auxiliary longitude and the free transfer time from a given initial orbit to geostationary orbit in a central Newtonian gravitational field is considered. The purpose of the optimization is to calculate the program of control of the vector of the thrust, which provided optimal multi-revolutionary trajectories to the final orbit with the minimum cost of the propellant. The magnitude of thrust is assumed to be constant. The optimized control is the vector control program of thrust, including its direction and periods of operation. For mathematical modeling of the spacecraft motion, differential equations in equinoctial elements are used, and as an independent variable, an auxiliary longitude is used, introduced in such a way that the differential equation for it coincides with the differential equation for true longitude in unperturbed motion. An approach based on the Pontryagin maximum principle is proposed to solve the trajectory optimization problem. Using the maximum principle, the problem of optimizing the multi-revolutionary transfer of spacecraft with limited thrust is reduced to a two-point boundary value problem and the boundary value problem is solved by the method of continuation on parameter. To get the goal, the problems of optimizing the multi-revolutionary transfer with limited power and limited thrust are considered. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
25. On equilibrium states of fluid membranes.
- Author
-
Olshanskii, Maxim A.
- Subjects
STATIC equilibrium (Physics) ,NAVIER-Stokes equations ,VECTOR fields ,EQUILIBRIUM ,DIFFERENTIAL equations ,AXIAL flow - Abstract
The paper studies the equilibrium configurations of inextensible elastic membranes exhibiting lateral fluidity. Using a continuum description of the membrane's motions based on the surface Navier–Stokes equations with bending forces, the paper derives differential equations governing the mechanical equilibrium. The equilibrium conditions are found to be independent of lateral viscosity and relate tension, pressure, and tangential velocity of the fluid. These conditions suggest that either the lateral fluid motion ceases or non-decaying stationary flow of mass can only be supported by surfaces with Killing vector fields, such as axisymmetric shapes. A shape equation is derived that extends the classical Helfrich model with an area constraint to membranes of non-negligible mass. Furthermore, the paper suggests a simple numerical method to compute solutions of the shape equation. Numerical experiments conducted reveal a diverse family of equilibrium configurations. The stability of equilibrium states involving lateral flow of mass remains an unresolved question. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
26. Solving the Biharmonic Equation in Irregular Domains by the Least Squares Collocation Method.
- Author
-
Belyaev, V. A. and Shapeev, V. P.
- Subjects
COLLOCATION methods ,BIHARMONIC equations ,DIFFERENTIAL equations ,LINEAR algebraic groups ,ALGEBRAIC equations ,ANALYTICAL solutions ,FINITE difference method - Abstract
This paper addresses a new version of the least squares collocation (LSC) method of high order accuracy proposed and implemented for the numerical solution of the nonhomogeneous biharmonic equation. The differential problem is projected onto a polynomial space of the fourth and eighth degrees by the LSC method. The algorithm implemented is applied in irregular domains. The boundaries of these domains are given by analytical curves, in particular, by splines. The irregular domain is embedded in a rectangle covered by a regular grid with rectangular cells. In this paper we use the irregular cells (i-cells) which are cut o by the domain boundary from the rectangular cells of the initial regular grid. The idea of attaching elongated i-cells to the neighboring ones is used. A separate piece of the analytical solution is constructed in the combined cells. The collocation and matching points located outside the domain are used to approximate the differential equations in the boundary cells. These two approaches allow us to reduce essentially the conditionality of the corresponding system of linear algebraic equations. It is shown that the approximate solutions obtained by the LSC method converge with an increased order and coincide with the analytical solutions of the test problems with high accuracy in the case of the known solution. The numerical results are compared with those found by other authors who used a high order finite difference method (FDM). The nonhomogeneous biharmonic equation is used to model the stress-strain state (SSS) of isotropic thin irregular plates as an application. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
27. Dynamics of gas bubble growth in a supersaturated solution with Sievert’s solubility law.
- Author
-
Gor, G. Yu. and Kuchma, A. E.
- Subjects
SOLUBILITY ,SOLUTION (Chemistry) ,DIFFERENTIAL equations ,ATMOSPHERIC water vapor ,NUCLEATION - Abstract
This paper presents a theoretical description of diffusion growth of a gas bubble after its nucleation in supersaturated liquid solution. We study systems where gas molecules completely dissociate in the solvent into two parts, thus making Sievert’s solubility law valid. We show that the difference between Henry’s and Sievert’s laws for chemical equilibrium conditions causes the difference in bubble growth dynamics. Assuming that diffusion flux is steady we obtain a differential equation on bubble radius. Bubble dynamics equation is solved analytically for the case of homogeneous nucleation of a bubble, which takes place at a significant pressure drop. We also obtain conditions of diffusion flux steadiness. The fulfillment of these conditions is studied for the case of nucleation of water vapor bubbles in magmatic melts. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
- View/download PDF
28. Application of evolutionary algorithms for the identification of the first-order differential equations systems.
- Author
-
Karaseva, Tatiana and Semenkin, Eugene
- Subjects
DIFFERENTIAL equations ,DIFFERENTIAL forms ,EVOLUTIONARY algorithms ,GENETIC programming ,NUMBER systems ,DIFFERENTIAL evolution - Abstract
The paper considers a new approach to the identification of dynamic objects in the form of the first-order differential equations system. The peculiarities of the proposed approach are the absence of restrictions on the structure of the differential equations included in the system and the symbolic representation of the obtained solution. The proposed approach includes a self-configuring genetic programming algorithm for selecting the structure of differential equations. The number of algorithms corresponds to the number of equations in the system. The method of differential evolution is used to optimize numeric constants. The authors apply a self-configuring procedure for the indicated evolutionary algorithms. The proposed approach has been tested on a variety of problems. The accuracy of the obtained solution has been investigated depending on the presence of noise in the sample data. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
29. Synchronization stability of power-grid-tied converters.
- Author
-
Ma, Rui, Zhang, Yayao, Yang, Ziqian, Kurths, Jürgen, Zhan, Meng, and Lin, Congping
- Subjects
SYNCHRONOUS generators ,SYNCHRONIZATION ,PHASE-locked loops ,POWER electronics ,DIFFERENTIAL equations ,RENEWABLE energy sources - Abstract
Synchronization stability is one of central problems in power systems, and it is becoming much more complicated with the high penetration of renewable energy and power electronics devices. In this paper, we review recent work by several nonlinear models for renewable-dominated power systems in terms of multiple timescales, in particular, grid-tied converters within the DC voltage timescale. For the simplest model, a second-order differential equations called the generalized swing equation by considering only the phase-locked loop (PLL) is obtained, which shows a similar form with the well-known swing equation for a synchronous generator in the traditional power systems. With more outer controllers included, fourth-order and fifth-order models can be obtained. The fourth-order model is called the extended generalized swing equation, exhibiting the combined function of grid synchronization and active power balance on the DC capacitor. In addition, a nonlinear model for a two coupled converter system is given. Based on these studies, we find that the PLL plays a key role in synchronization stability. In summary, the value of this paper is to clarify the key concept of the synchronization stability in renewable-dominated power systems based on different nonlinear models, which still lacks systematic studies and is controversial in the field of electrical power engineering. Meanwhile, it clearly uncovers that the synchronization stability of converters has its root in the phase synchronization concept in nonlinear sciences. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
30. Using transducerless time-domain thermoreflectance technique to measure in- and cross-plane thermal conductivity of nanofilms.
- Author
-
Du, Yanzheng, Bo, Zhenxing, Ma, Weigang, Wang, Weihua, and Zhang, Xing
- Subjects
- *
THERMAL conductivity , *NANOFILMS , *HEAT conduction , *THERMAL properties , *DIFFERENTIAL equations , *MULTILAYERED thin films - Abstract
Time-domain thermoreflectance (TDTR) and frequency-domain thermoreflectance techniques have been widely used to measure thermal properties. However, the existence of the metal sensor brings some limitations to the experimental measurement, such as temperature limits, disability to measure low in-plane thermal conductivity, in situ measurement cannot be achieved, etc. This paper proposes a transducerless time-domain thermoreflectance method to measure in- and cross-plane thermal conductivity of nanofilms, in which the optical absorption depth and thermal conductivity tensor are considered to establish a new differential equation that can describe the heat conduction process in multilayer structures. This thermal model can also calculate the effects of spot ellipticity and spot offset distance. Then, the analytical solution and relative deviation of this new model and the surface heat flow boundary model used in conventional TDTR are compared by calculating the phase signals. In terms of experimental measurement, this model is successfully used to derive cross- and in-plane thermal conductivity of PdSi and IrNiTa amorphous alloy nanofilms without a metal sensor. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
31. Solving the created ordinary differential equations from Lomax distribution.
- Author
-
Mohammed, Hussein Jabbar and Mohammed, Maha A.
- Subjects
CUMULATIVE distribution function ,DIFFERENTIAL equations ,HAZARD function (Statistics) ,ORDINARY differential equations - Abstract
This study presents a procedure to transfer a Lomax distribution into a class of ordinary differential equations. In this proposed designed some functions, which obtained from Lomax distribution, such as Survival function, cumulative distribution function, and hazard function are used. The aim of this research is to convert the Lomax distribution to the set of differential equations, then find the exact solutions for the created equations. Despite the availability of the exact solution and this is sufficient, the approximate solution, both analytical and numerical, remains a question that we discuss in this paper to study the types of solutions to these mentioned equations. an approximate solution is determined by analytically by Variation Iteration method (VIM) and numerically by Runge-Kutta of 4
th Order (RK4) method. Finally, a numerical illustration is also realized by utilizing MATLB 2016a, where the new results are shown. [ABSTRACT FROM AUTHOR]- Published
- 2022
- Full Text
- View/download PDF
32. Performance analysis of M/Ek/1 queue with working vacation, N-policy and customer impatience in transient mode.
- Author
-
Devi, V. N. Rama, Sridhar, G., and Chandan, K.
- Subjects
QUEUING theory ,PATIENCE ,CONSUMERS ,VACATIONS ,DIFFERENTIAL equations ,SENSITIVITY analysis - Abstract
This paper deals with the Markovian queueing system with working vacation in which the server may met with failures. There will be no delay in initiating repair. During this period any new customer is allowed to join the system. Each customer will be provided Erlangian phase service. Whenever the server finds nobody, the server goes for a working vacation during which the server provides service at a slower rate than the normal. Further, we considered two types of customer's impatience. We solved the system of differential equations to find Transient state probabilities and computed various performance indices of the queue. We then executed the sensitivity analysis and observed the impact on different parameters. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
33. Bernoulli wavelet technique in compution of solution of singular differential equation.
- Author
-
Yadav, Kailash, Piriadarshani, D., James, Beena, and Shekhar, Himanshu
- Subjects
- *
NUMERICAL solutions to differential equations , *DIFFERENTIAL equations - Abstract
In this paper the Bernoulli wavelets technique is applied to determine the numerical solution of singular ordinary differential equations. From a mathematical view, the suggested technique is straightforward as it provides precise data. According to this technique, the Bernoulli operational matrix is obtained from the Bernoulli function. The Bernoulli operational matrix constitutes a powerful means utilized in analyzing systems to identify the suitable numerical solutions to any differential equations. Numerical examples were give to support the effectiveness of the technique. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
34. Kinetics of nonisothermal phase change with arbitrary temperature–time history and initial transformed phase distributions.
- Author
-
Kangas, Joseph, Bischof, John C., and Hogan Jr., Christopher J.
- Subjects
NONLINEAR differential equations ,PARTIAL differential equations ,AVRAMI equation ,RATE of nucleation ,DIFFERENTIAL equations - Abstract
This paper describes the extension of the classic Avrami equation to nonisothermal systems with arbitrary temperature–time history and arbitrary initial distributions of transformed phase. We start by showing that through examination of phase change in Fourier space, we can decouple the nucleation rate, growth rate, and transformed fraction, leading to the derivation of a nonlinear differential equation relating these three properties. We then consider a population balance partial differential equation (PDE) on the phase size distribution and solve it analytically. Then, by relating this PDE solution to the transformed fraction of phase, we are able to derive initial conditions to the differential equation relating nucleation rate, growth rate, and transformed fraction. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
35. On Choosing a Value of Shape Parameter in Radial Basis Function Collocation Methods.
- Author
-
Krowiak, Artur and Podgórski, Jordan
- Subjects
RADIAL basis functions ,COLLOCATION methods ,NUMBER systems ,DIFFERENTIAL equations - Abstract
In the paper two approaches to determine a value of shape parameter for radial basis function collocation methods are presented. This value enables to achieve very accurate results in Kansa method and radial basis function-based pseudospectral one. Both approaches are based on the estimation of the condition number of the system matrix. One of them tries to find the value of shape parameter employing a heuristic that relates the condition number to computational precision, the other one searches for the largest value of this parameter that still ensures stable computation using geometrical dependence. The presented algorithms guarantee performing computation in the stable region and are more efficient than commonly used ones. Moreover they allow to automate the computational process for these methods. In the paper the algorithms are validated by a few differential equations using multiquadrics functions. The results show that the approaches lead to high accuracy especially when non-uniform grid is applied. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
36. An isolated line-shape model based on the Keilson and Storer function for velocity changes. I. Theoretical approaches.
- Author
-
Tran, H. and Hartmann, J.-M.
- Subjects
COLLISIONS (Physics) ,TEMPERATURE measurements ,DIFFERENTIAL equations ,MOLECULES ,LAGUERRE polynomials - Abstract
This paper presents new results for the modeling of isolated line shapes from the Doppler to the collisional regime, thus including the effects of confinement (Dicke narrowing) and of the speed dependence of collisional parameters. They are obtained within a classical description of the time evolution of the autocorrelation function of the optical transition moment, combined with the use of the Keilson and Storer model for the changes in the radiator translational velocity. A purely numerical solution to the subsequent differential equations, which uses discretized grids for the radiating-molecule velocity vector, is first described. An alternative approach, using projections onto generalized Laguerre polynomials (for the velocity modulus) and spherical harmonics (for the velocity orientation), is also presented. A first test of these approaches is made in the particular case of the Q(1) Raman line of the fundamental band of pure H
2 at room temperature (others will be presented in paper II). It is shown that the two models lead to exactly the same results, as expected, and to satisfactory agreement with measured values of the linewidth at various densities. [ABSTRACT FROM AUTHOR]- Published
- 2009
- Full Text
- View/download PDF
37. Second Symposium on “Recent Trends in the Numerical Solution of Differential Equations”: Preface.
- Author
-
Brugnano, Luigi
- Subjects
CONFERENCES & conventions ,NUMERICAL analysis ,DIFFERENTIAL equations ,MATHEMATICAL models ,DIFFERENTIABLE dynamical systems - Abstract
Information about the Recent Trends in the Numerical Solution of Differential Equations second symposium is presented. Topics discussed include the numerical method of Hamiltonian problems, new definition of stiffness with applications and numerical methods for variational inequalities. The meeting featured several mathematics experts, including L. Aceto, L. Brugnano and R. Lamour.
- Published
- 2009
- Full Text
- View/download PDF
38. Guaranteed feedback strategies versus best reply dynamics.
- Author
-
Krasovskii, Nikolay A., Tarasyev, Alexander M., and Tarasyev, Alexander A.
- Subjects
NASH equilibrium ,BOND market ,BEHAVIORAL assessment ,DIFFERENTIAL equations ,TIME perspective ,PSYCHOLOGICAL feedback - Abstract
The paper is devoted to the analysis of behavior of equilibrium trajectories in dynamic bimatrix games. We consider a system of differential equations which describe evolutionary dynamics of behavior of two players on the infinite time horizon. In the first case, we examine an approach based on the idea of guaranteed strategies in the sense of N.N. Krasovskii, for which the construction of the dynamic Nash equilibrium is implemented. In the second case, we consider a dynamic system based on the strategies of players' best replies. In this case, the equilibrium trajectory converges to the point of the static Nash equilibrium. For both cases, equilibrium trajectories are constructed and the comparison is carried out for the values of players' payoff functionals at the points of equilibrium. It is shown that characteristics of trajectories of the dynamic Nash equilibrium are better than properties of trajectories of the best reply dynamics. For demonstration of the behavior of equilibrium trajectories in the dynamic bimatrix games the model is presented in which we consider payoff matrices of two players on the financial markets of stocks and bonds. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
39. Analysis of the dissipativity of nonlinear differential systems using Lyapunov functions method.
- Author
-
Ekimov, A. V., Balykina, Yu. E., and Svirkin, M. V.
- Subjects
LYAPUNOV functions ,NONLINEAR systems ,NONLINEAR analysis ,DIFFERENTIAL equations - Abstract
The paper considers non-stationary systems of differential equations. The aim of this work is to obtain sufficient conditions for uniform dissipativity using the method of Lyapunov functions. The right side of the original system is presented as a sum of two terms: the first nonlinear approximation (unperturbed part) and its perturbation. For an exponentially stable unperturbed system, conditions are obtained for the order of perturbations under which the perturbed system has the property of uniform dissipativity. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
40. Extraction of parameters during signal radio profile processing in radiosensor diagnostics.
- Author
-
Boikov, K. A.
- Subjects
SCIENTIFIC literature ,VECTOR analysis ,DIFFERENTIAL equations ,ELECTRONIC equipment ,MODERN literature ,FOURIER transforms ,FREE flaps - Abstract
Modern methods of technical diagnostics, such as thermophysical diagnostics, vibrometry, boundary scanning, vector circuit analysis, have serious drawbacks. They are expressed in high inertia, distraction of processor time, or require galvanic contact with the object of study, which is often unacceptable. These shortcomings can be eliminated by passive radio-sensor technical diagnostics (PRTD), which uses its own radiation (signal radio profiles) to assess the technical condition of a radio-electronic device. In modern scientific literature, the issues of extracting the parameters of technical diagnostics of radio-electronic devices that it provides are practically not covered. The aim of the work is to study the extraction of the parameters of the signal radio profile and compare them with the parameters of radio electronic devices, the assessment of which can be provided by PRTD. Numerical modeling methods, methods of correlation analysis of the results were used to obtain signal radio profiles. In order to find the parameters of the signal radio profile, a mathematical method for solving differential equations was used. The paper presents an equation for the signal radio profile emitted by the electronic unit of the device, as well as an expression for its free components. The possibility of using a modified windowed Fourier transform to find the number of elementary components of a complex radio profile is shown, with an assessment of the correctness of the transformation at the initial stages of the analysis. A method for assessing the correctness of restoring the original signal radio profile is highlighted. A table of correspondence between the parameters of the radio-electronic device and the parameters of the signal radio profile is presented. The extraction of parameters opens up new possibilities in the field of studying the technical condition of radio electronic devices. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
41. Engineering method for solving boundary value problems.
- Author
-
Dalabaev, U. and Umarova, Sh
- Subjects
BOUNDARY value problems ,METHODS engineering ,ORDINARY differential equations ,ALGEBRAIC equations ,DIFFERENTIAL equations - Abstract
The paper proposes a simple approximate method for solving differential equations for boundary value problems. A method is proposed for averaging differential equations over a moving volume, which allows obtaining approximate analytical solutions of differential equations. The control volume is the only one in the considered area of the boundary value problem. In this case, the control volume is considered to be moved in the area under consideration. Based on the averaging of boundary value problems over the volume being moved, an algebraic equation is obtained. When averaging over one of the variables (in the case of a two-dimensional problem), ordinary differential equations are obtained. Examples are given. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
42. Analysis of a fluid queue modulated by a queue with vacations in random environment.
- Author
-
Sophia, Susairaj and Deepika, Babu Muthu
- Subjects
GENERATING functions ,VACATIONS ,DIFFERENTIAL equations ,FLUIDS - Abstract
A fluid queueing system fed by a single server vacation queue in a random environment is considered in this paper with the aim to investigate the buffer content distribution. The system of differential equations is solved using probability generating function technique and the buffer content distribution for the operative state and vacation state are determined. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
43. Application of Caputo differential equation in electrical circuits for different kinds of sources.
- Author
-
Maheswari, M., Piriadarshani, D., James, Beena, and Nishi, N. Daniya
- Subjects
DIFFERENTIAL equations ,STOCHASTIC models ,ELECTRIC circuits - Abstract
In this paper, different types of electrical circuits were modelled and their stochastic sources were computed for different kinds of sources using Caputo Fabrizio derivative. Numerical examples were given to support our results. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
44. Properties of κ-hypergeometric function and fractional derivatives.
- Author
-
Dang, Shruti, Mittal, Ekta, Joshi, Sunil, and Menon, Mudita
- Subjects
DIFFERENTIAL equations ,HYPERGEOMETRIC functions - Abstract
The object of this paper is to develop quardratic transformation of κ-hypergeometric differential equation and also develop new forms of quardratic transformation. Further we establish some properties of κ-hypergeometric function with κ-Caputo fractional derivative. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
45. A variant of an oscillation criterion for delayed second order half-linear differential equations.
- Author
-
Pátíková, Zuzana
- Subjects
LINEAR differential equations ,DIFFERENTIAL equations ,OSCILLATIONS ,DELAY differential equations - Abstract
The aim of this paper is to extend an oscillation criterion for the half-linear second order differential equations with delay to a more general form and to discuss relationship between these two variants and the link to the perturbation principle. The proving technique employs the Riccati transformation. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
46. Enhancing model identification with SINDy via nullcline reconstruction.
- Author
-
Prokop, Bartosz, Frolov, Nikita, and Gelens, Lendert
- Subjects
- *
DIFFERENTIAL equations , *PHASE space , *DYNAMICAL systems , *CUBIC equations , *SYSTEM identification , *LIMIT cycles , *IDENTIFICATION - Abstract
Many dynamical systems exhibit oscillatory behavior that can be modeled with differential equations. Recently, these equations have increasingly been derived through data-driven methods, including the transparent technique known as Sparse Identification of Nonlinear Dynamics (SINDy). This paper illustrates the importance of accurately determining the system's limit cycle position in phase space for identifying sparse and effective models. We introduce a method for identifying the limit cycle position and the system's nullclines by applying SINDy to datasets adjusted with various offsets. This approach is evaluated using three criteria: model complexity, coefficient of determination, and generalization error. We applied this method to several models: the oscillatory FitzHugh–Nagumo model, a more complex model consisting of two coupled cubic differential equations with a single stable state, and a multistable model of glycolytic oscillations. Our results confirm that incorporating detailed information about the limit cycle in phase space enhances the accuracy of model identification in oscillatory systems. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
47. Bifurcations of degenerate homoclinic solutions in discontinuous systems under non-autonomous perturbations.
- Author
-
Hua, Duo and Liu, Xingbo
- Subjects
- *
LYAPUNOV-Schmidt equation , *DIFFERENTIAL equations , *EQUATIONS - Abstract
The main aim of this paper is to study bifurcations of bounded solutions from a degenerate homoclinic solution for discontinuous systems under non-autonomous perturbations. We use Lyapunov–Schmidt reduction to give bifurcation equations and prove that a single parameter is enough to unfold two distinct homoclinic solutions bifurcated from the unperturbed degenerate homoclinic solution. Furthermore, we give an example of a periodically perturbed piecewise smooth differential equation in R 4 to support our conclusions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
48. Symbolic-Numeric Implementation of The Four Potential Method for Calculating Normal Modes of Square Electromagnetic Waveguide with Rectangular Insert.
- Author
-
Tiutiunnik, A. A. and Malykh, M. D.
- Subjects
GALERKIN methods ,ELECTROMAGNETIC waves ,WAVEGUIDES ,ELECTROMAGNETIC fields ,DIFFERENTIAL equations ,COMPUTER systems ,MAPLE - Abstract
In this paper, the Maple computer algebra system is used to construct a symbolic-numeric implementation of the method for calculating normal modes of square closed waveguides in a vector formulation. The method earlier proposed by Malykh et al. [M.D. Malykh, L.A. Sevastianov, A.A. Tiutiunnik, N.E. Nikolaev. On the representation of electromagnetic fields in closed waveguides using four scalar potentials // Journal of Electromagnetic Waves and Applications, 32 (7), 886-898 (2018)] will be referred to as the method of four potentials. The Maple system is used at all stages of treating the system of differential equations for four potentials: the generation of the Galerkin basis, the substitution of approximate solution into the system under study, the formulation of a computational problem, and its approximate solution. The paper presents the results of the verification method. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
49. Spectral Properties of One Elliptic Operator in a Punctured Domain.
- Author
-
Nalzhupbayeva, Gulzat
- Subjects
DIFFERENTIAL equations ,ELLIPTIC equations ,BOUNDARY value problems ,DERIVATIVES (Mathematics) ,HILBERT space - Abstract
In the work we derive regularized trace formulas which were established in papers of Kanguzhin and Tokmagambetov for the Laplace and m-Laplace operators in a punctured domain with the fixed iterating order m ∊ N. By using techniques of Sadovnichii and Lyubishkin, the authors in that papers described regularized trace formulae in the spatial dimension d = 2. In this note one claims that the formulas are also true for more general operators in the higher spatial dimensions, namely, 2 ≤ d ≤ 2m. Also, we give the further discussions on a development of the analysis associated with the operators in punctured domains. This can be done by using so called 'nonharmonic' analysis. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
50. A study of differential robot line-tracking based on visual recognition with segmented PID.
- Author
-
Zhou, Wenbo
- Subjects
- *
DIFFERENTIAL equations , *EQUATIONS of motion , *MOBILE robots , *ARTIFICIAL satellite tracking - Abstract
In the field of robot tracing, traditional sensors have the disadvantages of low accuracy, poor robustness, and expensive, which cannot meet the requirements of modern robot tracing. Based on the above analysis, this paper solves the equations of motion of differential wheeled robots, processes the visual sensor data through erosion and expansion operations to further acquire trajectories, and designs a segmented PID control system. Through repeated simulation experiments with ROS2 and gazebo simulation lines, we have come to the following conclusions: visual tracking has a better foresight, and can well solve the shortcomings of traditional sensors with low precision and poor sensitivity. The control error of the segmented PID control strategy is 50% of the traditional PID control strategy, and it can improve the response speed and robustness of the traditional PID. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
Discovery Service for Jio Institute Digital Library
For full access to our library's resources, please sign in.