28 results
Search Results
2. Analytical modeling and DEM analysis of soil–wheel interaction under cornering and skidding conditions in off-road vehicles
- Author
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Cheng Hu, Min Zhang, Jingwei Gao, Xuhong Tan, and Xiaobo Song
- Subjects
Normal force ,business.industry ,Rolling resistance ,Physics ,QC1-999 ,General Physics and Astronomy ,Drawbar pull ,Structural engineering ,Discrete element method ,Moment (mathematics) ,Slip ratio ,Slip angle ,business ,Mathematics ,Slip (vehicle dynamics) - Abstract
Soil–wheel interaction under cornering and slip conditions (SWICS) has a significant impact on the steering performance of off-road vehicles. In order to analyze the six-dimensional wheel forces in SWICS, a SWICS model based on the analytical method and the discrete element method (DEM) is developed in this paper. First, the modeling process of SWICS using the analytical method was detailed to predict the six-dimensional wheel forces in SWICS. The SWICS was then modeled using the DEM, which involved the following steps: (a) establishment of tire geometry, (b) selection of particle parameters, (c) parameter calibration, and (d) particle generation. Finally, DEM simulations were carried out for different slip angles and slip ratios under three loads, and the results were compared with those of the analytical model. The results show that the SWICS DEM model in this paper maintains a good fit with the analytical model, validating the efficiency of the DEM model and the parameter calibration method. The slip angle has a great influence on the lateral force, overturning moment, and aligning moment and a smaller impact on the normal force, drawbar pull, and rolling resistance moment. The slip ratio promotes an increase in the drawbar pull and rolling resistance moment but reduces the value of the lateral force and aligning moment. The research in this paper provides a DEM modeling approach and an analysis method for solving mechanical problems with different dimensions in SWICS, which will help improve the performance of off-road vehicles.
- Published
- 2021
3. Two effective computational schemes for a prototype of an excitable system
- Author
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Choonkil Park, Dianchen Lu, and Mostafa M. A. Khater
- Subjects
010302 applied physics ,Novelty ,Stability (learning theory) ,General Physics and Astronomy ,02 engineering and technology ,021001 nanoscience & nanotechnology ,01 natural sciences ,lcsh:QC1-999 ,Hamiltonian system ,Nonlinear system ,Contour line ,0103 physical sciences ,Applied mathematics ,0210 nano-technology ,Nonlinear evolution ,lcsh:Physics ,Mathematics - Abstract
In this article, two recent computational schemes [the modified Khater method and the generalized exp−φ(I)–expansion method] are applied to the nonlinear predator–prey system for constructing novel explicit solutions that describe a prototype of an excitable system. Many distinct types of solutions are obtained such as hyperbolic, parabolic, and rational. Moreover, the Hamiltonian system’s characteristics are employed to check the stability of the obtained solutions to show their ability to be applied in various applications. 2D, 3D, and contour plots are sketched to illustrate more physical and dynamical properties of the obtained solutions. Comparing our obtained solutions and that obtained in previous published research papers shows the novelty of our paper. The performance of the two used analytical schemes explains their effectiveness, powerfulness, practicality, and usefulness. In addition, their ability in employing various forms of nonlinear evolution equations is also shown.
- Published
- 2020
4. Stability of a general discrete-time viral infection model with humoral immunity and cellular infection
- Author
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M. A. Alshaikh and Ahmed M. Elaiw
- Subjects
010302 applied physics ,Lyapunov function ,General Physics and Astronomy ,02 engineering and technology ,021001 nanoscience & nanotechnology ,01 natural sciences ,Stability (probability) ,lcsh:QC1-999 ,symbols.namesake ,Immune system ,Discrete time and continuous time ,Stability theory ,Bounded function ,0103 physical sciences ,Humoral immunity ,symbols ,Applied mathematics ,0210 nano-technology ,Basic reproduction number ,lcsh:Physics ,Mathematics - Abstract
This paper studies the global stability of a general discrete-time viral infection model with virus-to-cell and cell-to-cell transmissions and with humoral immune response. We consider both latently and actively infected cells. The model incorporates three types of intracellular time delays. The production and clearance rates of all compartments as well as incidence rates of infection are modeled by general nonlinear functions. We use the nonstandard finite difference method to discretize the continuous-time model. We show that the solutions of the discrete-time model are positive and ultimately bounded. We derive two threshold parameters, the basic reproduction number R0 and the humoral immune response activation number R1, which completely determine the existence and stability of the model’s equilibria. By using Lyapunov functions, we have proven that if R0≤1, then the virus-free equilibrium Q0 is globally asymptotically stable; if R1≤1 1, then the persistent infection equilibrium with immune response Q¯ is globally asymptotically stable. We illustrate our theoretical results by using numerical simulations. The effects of antiretroviral drug therapy and time delay on the virus dynamics are also studied. We have shown that the time delay has a similar effect as the antiretroviral drug therapy.This paper studies the global stability of a general discrete-time viral infection model with virus-to-cell and cell-to-cell transmissions and with humoral immune response. We consider both latently and actively infected cells. The model incorporates three types of intracellular time delays. The production and clearance rates of all compartments as well as incidence rates of infection are modeled by general nonlinear functions. We use the nonstandard finite difference method to discretize the continuous-time model. We show that the solutions of the discrete-time model are positive and ultimately bounded. We derive two threshold parameters, the basic reproduction number R0 and the humoral immune response activation number R1, which completely determine the existence and stability of the model’s equilibria. By using Lyapunov functions, we have proven that if R0≤1, then the virus-free equilibrium Q0 is globally asymptotically stable; if R1≤1
- Published
- 2020
5. Hermite-Hadamard type inequalities pertaining conformable fractional integrals and their applications
- Author
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Yu Ming Chu, Muhammad Adil Khan, Sana Ullah, Arshad Iqbal, and Artion Kashuri
- Subjects
Pure mathematics ,Hermite polynomials ,010102 general mathematics ,Mathematics::Classical Analysis and ODEs ,General Physics and Astronomy ,Conformable matrix ,01 natural sciences ,Hermitian matrix ,Convexity ,lcsh:QC1-999 ,010101 applied mathematics ,Identity (mathematics) ,Hadamard transform ,Convex optimization ,0101 mathematics ,Convex function ,lcsh:Physics ,Mathematics - Abstract
In this paper, our main aim is to give results for conformable fractional integral version of Hermite-Hadamard inequality and their applications for mid-point formula and means. First, we prove an identity associated with the Hermite-Hadamard inequality for conformable fractional integrals. By using this identity and convexity of different classes of functions and some well-known inequalities, we obtain several results for the inequality. At the end, we also present applications for some error estimations of the mid-point formula and means. The results obtained in this paper generalize the earlier results. Furthermore, the identity can be used to obtain results for Hermite-Hadamard inequality for some other generalized classes of convex functions.
- Published
- 2018
6. Accurate off-axis magnetic field calculation of axisymmetric cylindrical current distributions
- Author
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G. Mehrshahi and Shokrollah Karimian
- Subjects
Series (mathematics) ,Numerical analysis ,Physics ,QC1-999 ,Mathematical analysis ,Rotational symmetry ,Range (statistics) ,General Physics and Astronomy ,Function (mathematics) ,Current density ,Finite element method ,Mathematics ,Magnetic field - Abstract
This paper proposes an accurate, simple, and versatile approach for calculation of the off-axis magnetic field of any axisymmetric cylindrical current distribution, eliminating the need for complicated elliptical integrals and sophisticated numerical methods, e.g., finite element method. The results obtained from both integral and series forms not only confirm the validity of the proposed method against well-established analytical techniques but also outperform them in terms of accuracy, simplicity, and calculation time. The integral method yields greater convergence (14 decimal places) compared to the ill-posed series method, which depends on the highest order of derivatives; this would yield an error below 1% at the highest order of derivatives (i.e., 14 for axial-H and 11 for radial-H in the range of 0 < ρ < 0.8R). The off-axis solution to the case of a thin shell of finite length with cylindrical current distribution is calculated using the proposed method irrespective of the current density function, though only the most common case of uniform current has been included in the solved special cases. Given that no known formula is available to solve this case, the results of this work have been validated against the results of the well-known software ANSYS Maxwell simulator.
- Published
- 2021
7. Plenty accurate soliton wave solutions of the prototype of an excitable system
- Author
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Samir A. Salama, S. H. Alfalqi, Ying-Fang Zhang, J. F. Alzaidi, and Mostafa M. A. Khater
- Subjects
Nonlinear system ,Numerical analysis ,Contour line ,Physics ,QC1-999 ,Radar chart ,General Physics and Astronomy ,Applied mathematics ,Mathematics ,Variable (mathematics) - Abstract
In this paper, the nonlinear fractional Lotka–Volterra model is analyzed and numerically studied. This research is based on applying the three latest analytical schemes and three other numerical schemes to construct rich wave solutions. In different forms, many novel solitary wave solutions are built and presented in two-dimensional, three-dimensional, and contour plots. The numerical method conditions are evaluated through the obtained analytical solutions, and the accuracy of the analytical solutions is studied. Many numerical solutions are constructed based on the employed schemes. Additionally, the analytical, semi-analytical, numerical, and absolute values of error between the values of obtained solutions are calculated with the different values of the given variable in the solutions. Furthermore, the match between the obtained analytical solution and the numerical solution has been explained through some two-dimensional distributed radar charts. The contribution of this article is demonstrated by comparing the obtained solution with the recently published results of the same model.
- Published
- 2021
8. Numerical solution of convection–diffusion–reaction equations by a finite element method with error correlation
- Author
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Md. Kamrujjaman, Md. Shafiqul Islam, and Sadia Akter Lima
- Subjects
Correlation ,Nonlinear system ,Numerical analysis ,Physics ,QC1-999 ,Convergence (routing) ,General Physics and Astronomy ,Applied mathematics ,Dissipation ,Convection–diffusion equation ,Stability (probability) ,Finite element method ,Mathematics - Abstract
This study contemplates the Finite Element Method (FEM), a well-known numerical method, to find numerical approximations of the Convection–Diffusion–Reaction (CDR) equation. We concentrate on analyzing the convergence and stability of the nonlinear parabolic partial equations. The method is generally applied without truncating the nonlinear terms and avoiding restrictive assumptions. Regular and irregular geometrical shapes are the key objective of this research paper. This study also focuses on the accuracy and acceptance of the FEM method by utilizing dissipation error, dispersion error, and total error analysis. The results are portrayed both graphically and in a tabular form, which virtually ensures the method’s validity and the algorithm’s efficiency to sustain the accuracy, simplicity, and applicability for solving nonlinear CDR equations. The proposed technique may also be applied for solving any nonlinear reaction–diffusion equations.
- Published
- 2021
9. Estimating the demagnetization factors for regular permanent magnet pieces
- Author
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Christian R.H. Bahl
- Subjects
Simple (abstract algebra) ,Magnet ,Physics ,QC1-999 ,Demagnetizing field ,General Physics and Astronomy ,Applied mathematics ,Numerical modeling ,High resolution ,Mathematics - Abstract
In this paper, methods for finding the demagnetization factor, specifically for permanent magnets, are considered and compared. Widely applied and cited literature expressions are compared to high resolution numerical modeling in order to establish the applicability of the expressions. Overall, the expressions are found to be very closely correlated with the modeling results. In the second part, a simple geometrically based method to find the demagnetization factor is proposed and compared to the numerical modeling results. Fairly good correspondence is found, indicating the applicability of this simple method.
- Published
- 2021
10. The stability optimization algorithm of second-order magnetic gradient tensor
- Author
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Qingzhu Li, Guoquan Ren, Bo Wang, and Zhining Li
- Subjects
Mean squared error ,Physics ,QC1-999 ,Finite difference ,General Physics and Astronomy ,Order (group theory) ,Magnetic gradient ,Tensor ,Stability (probability) ,Algorithm ,Noise (electronics) ,Electromagnetic interference ,Mathematics - Abstract
In order to improve the stability of the second-order magnetic gradient tensor data under magnetic interference, a stability optimization algorithm based on the improved central difference method is proposed in this paper, and a new measuring device is designed according to the new algorithm. In the simulation, the root mean square error (RMSE) of the old and new methods under different noise conditions is studied, and the results show that the proposed method is more stable. In the experiment, the measurement was carried out in a site with complex magnetic interference, and the positioning results were analyzed through the RMSE. The RMSE of the positioning results obtained by the traditional method and the proposed method was (3.3782, 1.3482, 0.3337) and (0.3988, 0.0070, 0.0510), respectively. The simulation and the experiment showed the superiority of the proposed method.
- Published
- 2021
11. Arbitrary degree distribution networks with perturbations
- Author
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Xiaomin Wang, Fei Ma, and Bing Yao
- Subjects
010302 applied physics ,Vertex (graph theory) ,Exponential distribution ,Degree (graph theory) ,Distribution (number theory) ,Generating function ,General Physics and Astronomy ,02 engineering and technology ,Complex network ,021001 nanoscience & nanotechnology ,Poisson distribution ,Degree distribution ,01 natural sciences ,lcsh:QC1-999 ,symbols.namesake ,0103 physical sciences ,symbols ,Statistical physics ,0210 nano-technology ,lcsh:Physics ,Mathematics - Abstract
Complex networks have played an important role in the field of natural science and social science, attracting considerable attention of more and more scholars. Currently, scholars have proposed numbers of complex networks, in which some show a required degree distribution and others follow arbitrary degree distribution. The goal of this paper is to discuss the impact of perturbations on degree distribution. To this end, we first introduce two types of perturbations, i.e., edge perturbations and vertex perturbations, and investigate networks whose structure can be determined by tuning perturbation rules. Next, we calculate the degree distribution using two popularly utilized mathematical methods, namely, rate equation and generating function. Afterward, we analyze several networks with different degree distributions, for example, Poisson distribution, stretched exponential distribution, and power-law distribution; there are, in practice, some pronounced differences among three cases. Therefore, to a certain extent, the above three cases can serve as the measures for degree distribution to help us clearly distinguish among different degree distributions.
- Published
- 2021
12. The general bilinear techniques for studying the propagation of mixed-type periodic and lump-type solutions in a homogenous-dispersive medium
- Author
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Dumitru Baleanu, Mohamed S. Osman, Jian-Guo Liu, Wen-Hui Zhu, and Li Zhou
- Subjects
010302 applied physics ,Mathematical analysis ,General Physics and Astronomy ,Mixed type ,Bilinear interpolation ,02 engineering and technology ,Bilinear form ,Type (model theory) ,021001 nanoscience & nanotechnology ,Dispersive medium ,01 natural sciences ,lcsh:QC1-999 ,Transformation (function) ,Nonlinear Sciences::Exactly Solvable and Integrable Systems ,0103 physical sciences ,Fluid dynamics ,0210 nano-technology ,lcsh:Physics ,Mathematics ,Free parameter - Abstract
This paper aims to construct new mixed-type periodic and lump-type solutions via dependent variable transformation and Hirota’s bilinear form (general bilinear techniques). This study considers the (3 + 1)-dimensional generalized B-type Kadomtsev–Petviashvili equation, which describes the weakly dispersive waves in a homogeneous medium in fluid dynamics. The obtained solutions contain abundant physical structures. Consequently, the dynamical behaviors of these solutions are graphically discussed for different choices of the free parameters through 3D plots.
- Published
- 2020
13. The numerical solution of fourth order nonlinear singularly perturbed boundary value problems via 10-point subdivision scheme based numerical algorithm
- Author
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Yu-Ming Chu, Dumitru Baleanu, Safia Malik, Syeda Tehmina Ejaz, and Ghulam Mustafa
- Subjects
010302 applied physics ,business.industry ,MathematicsofComputing_NUMERICALANALYSIS ,General Physics and Astronomy ,Order (ring theory) ,02 engineering and technology ,Computer Science::Computational Geometry ,021001 nanoscience & nanotechnology ,01 natural sciences ,lcsh:QC1-999 ,Nonlinear system ,Scheme (mathematics) ,0103 physical sciences ,Polygon ,Convergence (routing) ,Point (geometry) ,Boundary value problem ,0210 nano-technology ,business ,Algorithm ,lcsh:Physics ,Mathematics ,Subdivision ,ComputingMethodologies_COMPUTERGRAPHICS - Abstract
The subdivision scheme is used to illustrate smooth curves and surfaces. It is an algorithmic technique which takes a coarse polygon as an input and produces a refined polygon as an output. In this paper, a 10-point interpolating subdivision scheme is used to develop a numerical algorithm for the solution of fourth order nonlinear singularly perturbed boundary value problems (NSPBVPs). The studies of convergence and approximation order of the numerical algorithm are also presented. The solution of NSPBVPs is presented to see the efficiency of the algorithm.
- Published
- 2020
14. Chaos and control of a three-dimensional fractional order discrete-time system with no equilibrium and its synchronization
- Author
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Shaher Momani, Amina Aicha Khennaoui, Giuseppe Grassi, Adel Ouannas, and Viet-Thanh Pham
- Subjects
010302 applied physics ,Phase portrait ,General Physics and Astronomy ,02 engineering and technology ,Lyapunov exponent ,021001 nanoscience & nanotechnology ,Bifurcation diagram ,01 natural sciences ,Synchronization ,lcsh:QC1-999 ,Nonlinear system ,symbols.namesake ,Control theory ,Stability theory ,0103 physical sciences ,Attractor ,symbols ,Applied mathematics ,0210 nano-technology ,lcsh:Physics ,Mathematics - Abstract
Chaotic systems with no equilibrium are a very important topic in nonlinear dynamics. In this paper, a new fractional order discrete-time system with no equilibrium is proposed, and the complex dynamical behaviors of such a system are discussed numerically by means of a bifurcation diagram, the largest Lyapunov exponents, a phase portrait, and a 0–1 test. In addition, a one-dimensional controller is proposed. The asymptotic convergence of the proposed controller is established by means of the stability theory of linear fractional order discrete-time systems. Next, a synchronization control scheme for two different fractional order discrete-time systems with hidden attractors is reported, where the master system is a two-dimensional system that has been reported in the literature. Numerical results are presented to confirm the results.
- Published
- 2020
15. Approximately h-preinvex functions, associated Hermite–Hadamard-like inequality, new q-identity, and estimation of its bounds with applications
- Author
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Muhammad Uzair Awan, Sadia Talib, Muhammad Aslam Noor, and Khalida Inayat Noor
- Subjects
010302 applied physics ,Pure mathematics ,Class (set theory) ,Hermite polynomials ,General Physics and Astronomy ,02 engineering and technology ,Function (mathematics) ,021001 nanoscience & nanotechnology ,01 natural sciences ,lcsh:QC1-999 ,Identity (mathematics) ,Hadamard transform ,0103 physical sciences ,0210 nano-technology ,Quantum ,lcsh:Physics ,Mathematics - Abstract
The main objective of this paper is to introduce and investigate a new class of preinvex functions, called approximately h-preinvex functions, which depend on a given bifunction e(·, ·). It is observed that this class includes several other new and known classes of preinvexity. We derive a new refinement of Hermite–Hadamard-like inequalities using the class of approximately preinvex functions. We also derive a new q-integral identity using the q-differentiable function. Using this auxiliary result, we obtain several new estimates of quantum bounds. We also discuss several new special cases of the obtained results. Certain applications of the main results are also discussed.
- Published
- 2020
16. A family of exact models for radiating matter
- Author
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Sunil D. Maharaj, R. Narain, and A. B. Mahomed
- Subjects
010302 applied physics ,General Physics and Astronomy ,Charge (physics) ,02 engineering and technology ,Cosmological constant ,Function (mathematics) ,021001 nanoscience & nanotechnology ,01 natural sciences ,lcsh:QC1-999 ,Bernoulli's principle ,Transformation (function) ,0103 physical sciences ,Riccati equation ,Applied mathematics ,Boundary value problem ,0210 nano-technology ,lcsh:Physics ,Generating function (physics) ,Mathematics - Abstract
In this paper, the cosmological constant and electric charge are incorporated in the Einstein–Maxwell field equations. Two approaches are used to investigate the problem. First, the boundary condition is expressed as a generalized Riccati equation in one of the gravitational potentials. New classes of exact solutions are found by writing the Riccati equation in linear, Bernoulli, and inhomogeneous forms. Our solutions contain previous results in the absence of the cosmological constant and charge. Second, it is possible to preserve the form of the generalized Riccati equation by introducing a transformation called the horizon function. This transformation simplifies the generalized Riccati equation. We generate new solutions to the transformed Riccati equation when one of the metric functions serves as a generating function. We also obtain other families of new classes of exact solutions, where the horizon function serves as a generating function. Interestingly, new uncharged solutions, not contained in previous studies, arise as special cases of the inhomogeneous Riccati equation in both approaches.
- Published
- 2020
17. Numerical analysis of Williamson fluid flow along an exponentially stretching cylinder
- Author
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Mudassar Jalil, Muhammad Nawaz Naeem, and Waheed Iqbal
- Subjects
010302 applied physics ,Partial differential equation ,business.industry ,Numerical analysis ,Mathematical analysis ,General Physics and Astronomy ,02 engineering and technology ,Computational fluid dynamics ,021001 nanoscience & nanotechnology ,01 natural sciences ,lcsh:QC1-999 ,Physics::Fluid Dynamics ,Flow (mathematics) ,Parasitic drag ,0103 physical sciences ,Fluid dynamics ,Compressibility ,Cylinder ,0210 nano-technology ,business ,lcsh:Physics ,Mathematics - Abstract
The present paper presents a mathematical probe for incompressible steady two-dimensional flow of Williamson fluid along an exponentially stretching cylinder. Derived PDEs for this work are changed into ODEs by adopting right transformations. Then numerical procedure is carried out by Shooting Technique in accordance with the RK-Method of order six. The influence of the Reynold’s number and Weissenberg’s numbers on the velocity profile is analyzed, and the variation in skin friction coefficient is explored. The results are elaborated upon through graphs and tables. The validity of the results is presented by comparing them with the previous works.
- Published
- 2019
18. High-order accurate and high-speed calculation system of 1D Laplace and Poisson equations using the interpolation finite difference method
- Author
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Tsugio Fukuchi
- Subjects
010302 applied physics ,Laplace transform ,Computation ,Numerical analysis ,Lagrange polynomial ,Finite difference method ,General Physics and Astronomy ,02 engineering and technology ,Function (mathematics) ,021001 nanoscience & nanotechnology ,01 natural sciences ,lcsh:QC1-999 ,symbols.namesake ,0103 physical sciences ,symbols ,Applied mathematics ,Poisson's equation ,0210 nano-technology ,lcsh:Physics ,Interpolation ,Mathematics - Abstract
Among the methods of the numerical analysis of the physical phenomena of the continuum, the finite difference method (FDM) is the first examined method and has been established as a full numerical calculation system over the regular domain. However, there is a general perception that generality in numerical calculations cannot be expected over complex irregular domains. As using the FDM, the development of computational methods that are applicable over any irregular domain is considered to be a very important contemporary problem. In the FDM, there is a marked characteristic that the theory developed by the (spatial) one-dimensional (1D) problem is naturally applied to the 2D and 3D problems. The calculation method is called the interpolation FDM (IFDM). In this paper, attention is paid to 1D Laplace and Poisson equations, and the whole image of the IFDM using the algebraic polynomial interpolation method (APIM), the IFDM-APIM, is described. Based on the Lagrange interpolation function, the spatial difference schemes from 2nd order to 10th order including odd order are calculated and defined instantaneously over equally/unequally spaced grid points, then, high-order accurate and high-speed computations become possible.
- Published
- 2019
19. Dynamical analysis of cigarette smoking model with a saturated incidence rate
- Author
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Anwar Zeb, Gul Zaman, Ebraheem O. Alzahrani, and Ayesha Bano
- Subjects
Hopf bifurcation ,Steady state (electronics) ,Differential equation ,010102 general mathematics ,Finite difference ,General Physics and Astronomy ,01 natural sciences ,lcsh:QC1-999 ,010305 fluids & plasmas ,symbols.namesake ,Exponential stability ,Cigarette smoking ,0103 physical sciences ,symbols ,Applied mathematics ,0101 mathematics ,Logistic function ,MATLAB ,computer ,lcsh:Physics ,Mathematics ,computer.programming_language - Abstract
In this paper, we consider a delayed smoking model in which the potential smokers are assumed to satisfy the logistic equation. We discuss the dynamical behavior of our proposed model in the form of Delayed Differential Equations (DDEs) and show conditions for asymptotic stability of the model in steady state. We also discuss the Hopf bifurcation analysis of considered model. Finally, we use the nonstandard finite difference (NSFD) scheme to show the results graphically with help of MATLAB.
- Published
- 2018
20. Numerical solution of the unsteady diffusion-convection-reaction equation based on improved spectral Galerkin method
- Author
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Yuzhe Zhang, Cheng Zeng, Yupeng Yuan, Ye Zhang, and Jiaqi Zhong
- Subjects
0209 industrial biotechnology ,Truncation ,General Physics and Astronomy ,02 engineering and technology ,01 natural sciences ,Chemical equation ,Finite element method ,lcsh:QC1-999 ,010305 fluids & plasmas ,020901 industrial engineering & automation ,Ordinary differential equation ,0103 physical sciences ,Applied mathematics ,Boundary value problem ,Galerkin method ,Fourier series ,Eigenvalues and eigenvectors ,lcsh:Physics ,Mathematics - Abstract
The aim of this paper is to present an explicit numerical algorithm based on improved spectral Galerkin method for solving the unsteady diffusion-convection-reaction equation. The principal characteristics of this approach give the explicit eigenvalues and eigenvectors based on the time-space separation method and boundary condition analysis. With the help of Fourier series and Galerkin truncation, we can obtain the finite-dimensional ordinary differential equations which facilitate the system analysis and controller design. By comparing with the finite element method, the numerical solutions are demonstrated via two examples. It is shown that the proposed method is effective.
- Published
- 2018
21. Numerical approach based on Bernstein polynomials for solving mixed Volterra-Fredholm integral equations
- Author
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Muhammad Omar, Haziqa Komal, Ghulam Mustafa, and Faheem Khan
- Subjects
Approximation theory ,Discretization ,General Physics and Astronomy ,010103 numerical & computational mathematics ,01 natural sciences ,Parabolic partial differential equation ,Integral equation ,Bernstein polynomial ,lcsh:QC1-999 ,010101 applied mathematics ,Convergence (routing) ,Applied mathematics ,Boundary value problem ,0101 mathematics ,Representation (mathematics) ,lcsh:Physics ,Mathematics - Abstract
This paper provides an effective numerical technique for obtaining the approximate solution of mixed Volterra-Fredholm Integral Equations (VFIEs) of second kind. The VFIEs arise from parabolic boundary value problems, mathematical modelling of the spatio-temporal development of an epidemic, and from various physical and Engineering models. The proposed method is based on the discretization of VFIEs by Bernstein’s approximation. Some results on convergence are also established which suggests that the technique converges to a smooth approximate solution. Its remarkable accuracy properties are finally demonstrated by several examples with graphical representation.
- Published
- 2017
22. Stability of CTL immunity pathogen dynamics model with capsids and distributed delay
- Author
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A. S. Alofi, Ahmed M. Elaiw, and N. H. AlShamrani
- Subjects
Lyapunov function ,Time delays ,010102 general mathematics ,Dynamics (mechanics) ,General Physics and Astronomy ,01 natural sciences ,Stability (probability) ,lcsh:QC1-999 ,Quantitative Biology::Cell Behavior ,010101 applied mathematics ,CTL ,symbols.namesake ,symbols ,Applied mathematics ,0101 mathematics ,lcsh:Physics ,Mathematics ,Cellular biophysics - Abstract
In this paper, a pathogen dynamics model with capsids and saturated incidence has been proposed and analyzed. Cytotoxic T Lymphocyte (CTL) immune response and two distributed time delays have been incorporated into the model. The nonnegativity and boundedness of the solutions of the proposed model have been shown. Two threshold parameters which fully determine the existence and stability of the three steady states of the model have been computed. Using the method of Lyapunov function, the global stability of the steady states of the model has been established. The theoretical results have been confirmed by numerical simulations.
- Published
- 2017
23. Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term
- Author
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Shahid Hasnain, D. S. Mashat, and Muhammad Saqib
- Subjects
Numerical analysis ,010102 general mathematics ,Finite difference method ,Finite difference ,General Physics and Astronomy ,01 natural sciences ,lcsh:QC1-999 ,010305 fluids & plasmas ,Alternating direction implicit method ,Approximation error ,0103 physical sciences ,Reaction–diffusion system ,Initial value problem ,Applied mathematics ,Boundary value problem ,0101 mathematics ,lcsh:Physics ,Mathematics - Abstract
This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.
- Published
- 2017
24. Derivation and application of mathematical model for well test analysis with variable skin factor in hydrocarbon reservoirs
- Author
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Yuwei Jiao, Aifang Bie, Jing Xia, Wenhui Li, and Pengcheng Liu
- Subjects
Logarithm ,Laplace transform ,integumentary system ,020209 energy ,General Physics and Astronomy ,02 engineering and technology ,lcsh:QC1-999 ,Permeability (earth sciences) ,020401 chemical engineering ,Well test analysis ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,Skin factor ,0204 chemical engineering ,Type curve ,lcsh:Physics ,Dimensionless quantity ,Test data ,Mathematics - Abstract
Skin factor is often regarded as a constant in most of the mathematical model for well test analysis in oilfields, but this is only a kind of simplified treatment with the actual skin factor changeable. This paper defined the average permeability of a damaged area as a function of time by using the definition of skin factor. Therefore a relationship between a variable skin factor and time was established. The variable skin factor derived was introduced into existing traditional models rather than using a constant skin factor, then, this newly derived mathematical model for well test analysis considering variable skin factor was solved by Laplace transform. The dimensionless wellbore pressure and its derivative changed with dimensionless time were plotted with double logarithm and these plots can be used for type curve fitting. The effects of all the parameters in the expression of variable skin factor were analyzed based on the dimensionless wellbore pressure and its derivative. Finally, actual well testing data were used to fit the type curves developed which validates the applicability of the mathematical model from Sheng-2 Block, Shengli Oilfield, China.
- Published
- 2016
25. Numerical simulation of two dimensional sine-Gordon solitons using modified cubic B-spline differential quadrature method
- Author
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Mohammad Tamsir, H. S. Shukla, and Vineet K. Srivastava
- Subjects
General Physics and Astronomy ,Tanh-sinh quadrature ,Gauss–Kronrod quadrature formula ,lcsh:QC1-999 ,Numerical integration ,Mathematics::Numerical Analysis ,symbols.namesake ,Ordinary differential equation ,Runge–Kutta method ,symbols ,Gauss–Jacobi quadrature ,Nyström method ,Applied mathematics ,lcsh:Physics ,Numerical stability ,Mathematics - Abstract
In this paper, a modified cubic B-spline differential quadrature method (MCB-DQM) is employed for the numerical simulation of two-space dimensional nonlinear sine-Gordon equation with appropriate initial and boundary conditions. The modified cubic B-spline works as a basis function in the differential quadrature method to compute the weighting coefficients. Accordingly, two dimensional sine-Gordon equation is transformed into a system of second order ordinary differential equations (ODEs). The resultant system of ODEs is solved by employing an optimal five stage and fourth-order strong stability preserving Runge–Kutta scheme (SSP-RK54). Numerical simulation is discussed for both damped and undamped cases. Computational results are found to be in good agreement with the exact solution and other numerical results available in the literature.
- Published
- 2015
26. Numerical solution of two dimensional coupled viscous Burger equation using modified cubic B-spline differential quadrature method
- Author
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Jai Kumar, Mohammad Tamsir, Hari S. Shukla, and Vineet K. Srivastava
- Subjects
B-spline ,General Physics and Astronomy ,Basis function ,Numerical Analysis (math.NA) ,lcsh:QC1-999 ,Burgers' equation ,Runge–Kutta methods ,Nonlinear system ,Ordinary differential equation ,FOS: Mathematics ,Applied mathematics ,Nyström method ,Mathematics - Numerical Analysis ,Boundary value problem ,65M70 ,lcsh:Physics ,Mathematics - Abstract
In this paper, a numerical solution of the two dimensional nonlinear coupled viscous Burgers equation is discussed with the appropriate initial and boundary conditions using the modified cubic B spline differential quadrature method. In this method, the weighting coefficients are computed using the modified cubic B spline as a basis function in the differential quadrature method. Thus, the coupled Burgers equations are reduced into a system of ordinary differential equations (ODEs). An optimal five stage and fourth order strong stability preserving Runge Kutta scheme is applied to solve the resulting system of ODEs. The accuracy of the scheme is illustrated via two numerical examples. Computed results are compared with the exact solutions and other results available in the literature. Numerical results show that the MCB DQM is efficient and reliable scheme for solving the two dimensional coupled Burgers equation., Comment: 15 pages, 3 figures
- Published
- 2014
27. Traveling wave solution of fractional KdV-Burger-Kuramoto equation describing nonlinear physical phenomena
- Author
-
A. K. Gupta and S. Saha Ray
- Subjects
Legendre wavelet ,Numerical analysis ,General Physics and Astronomy ,Dissipation ,Instability ,lcsh:QC1-999 ,Nonlinear system ,Nonlinear Sciences::Exactly Solvable and Integrable Systems ,Simple (abstract algebra) ,Applied mathematics ,Dispersion (water waves) ,Korteweg–de Vries equation ,lcsh:Physics ,Mathematics - Abstract
In this paper, KdV-Burger-Kuramoto equation involving instability, dissipation, and dispersion parameters is solved numerically. The numerical solution for the fractional order KdV-Burger-Kuramoto (KBK) equation has been presented using two-dimensional Legendre wavelet method. The approximate solutions of nonlinear fractional KBK equation thus obtained by Legendre wavelet method are compared with the exact solutions. The present scheme is very simple, effective and convenient for obtaining numerical solution of the KBK equation.
- Published
- 2014
28. Numerical calculation of fully-developed laminar flows in arbitrary cross-sections using finite difference method
- Author
-
Tsugio Fukuchi
- Subjects
Mathematical analysis ,Finite difference method ,General Physics and Astronomy ,Finite difference coefficient ,Laminar flow ,Mixed finite element method ,Boundary knot method ,Finite element method ,lcsh:QC1-999 ,Regular grid ,Physics::Fluid Dynamics ,lcsh:Physics ,Mathematics ,Extended finite element method - Abstract
The finite difference method has adequate accuracy to calculate fully-developed laminar flows in regular cross-sectional domains, but in irregular domains such flows are solved using the finite element method or structured grids. However, it has become apparent that we can use the finite difference method freely even if domains are complex. The non-slip condition on the wall must be imposed. Even in irregular domains, this boundary condition can be introduced indirectly by adding a single procedure to set the boundary condition. The calculations have similar accuracy as in regular domains. The proposed method has a wide range of applications; as a first step, fully-developed laminar flows are investigated in the paper.
- Published
- 2011
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