Search

In this study, we will discuss numerical solutions of conformable fractional systems of second-order integrodifferential equations concerning couple types Volterra and Fredholm. These conformable fractional systems will be considered in the sense of periodic boundary conditions in two points. The reproducing kernel Hilbert space method is used with the help of Mathematica 11 to utilize different tabulated data and graphical results. Series representation and required theorems are utilized and proved in the constructed Hilbert spaces. Several applications of linear and nonlinear function types have been studied and solved to ensure the applicability and power of the method. From the gained results, one can note that the approach algorithm is accurate and provides numerical results in a faster time and with less effort. Several notes and highlights with the latest references are discussed and presented at the end of the article.

In this work, the Optimal Homotopy Asymptotic Method (OHAM) is prolifically implemented to find the optimal solutions of fractional order of fuzzy differential equations. We inspect the competence of the method by examining fractional order time-dependent first order fuzzy initial value problems in the Caputo derivative sense. The concepts of fuzzy sets theory and fractional calculus were used to present a new general fuzzification formulation of the OHAM method followed by fuzzy analysis for the proposed fractional problems are presented in detail. OHAM is recognized as a feasible and convergent method for solving linear and nonlinear models, and it provides a convenient technique for controlling the convergence of approximate solutions optimally. The method's capability is demonstrated by obtaining approximate solutions to linear and nonlinear fuzzy initial value problems in various orders of fractional derivative. The numerical results acknowledge that OHAM is a feasible and transformation mechanism for solving linear and nonlinear fuzzy fractional initial value problems. Also, the results ensure that the method used was succinct, efficient, and simple to use, to deal with a more comprehensive fuzzy fractional differential equation.

Convection differential equations that include momentum, energy and mass balance equations are used for the simulations of boundary layer (BL) flows. In convection analysis, it is in execution to dimensionless the BL system through similarity variable. However, a wide range of convection differential equations cannot be non-dimensionalized using similarity variable therefore the intent of this manuscript is to develop non-similar model for the forced convective magnetic flow of a viscous fluid above an exponentially expanding surface saturated by nano-fluid. The non-similarity is due to the exponential stretching of the surface and viscous dissipation. Influences of chemical reaction and heat generation are also incorporated. The non-similarity transformation is applied to the nonlinear partial differential system (PDE’s) to transform them into dimensionless PDE’s. Non-similar system is analytically approximated by adapting local non-similarity (LNS) and then it is numerically simulated by finite difference based bvp4c algorithm to explore the influences of significant numbers named as Prandlt number, chemical reaction, magnetic field, Brownian motion, heat generation, Eckert number, thermophoresis on concentration, velocity and temperature distribution. Auxiliary consequences presume that the heat penetration in fluid rises with enhancements in Brownian motion and Prandtl number, while it can be perceived here that for positive estimations of heat generation causes the thicker temperature field. Increasing non-similarity variable and magnetic number become reason for the reduction of temperature profile and chemical reaction is reason of reduced concentration profile.

This communication highlights the thermal characterization of Ree-Eyring fluid with entropy generation and nonlinear heat source/sink confined by double rotating disk. The classical significances of Joule heating and homogenous/heterogeneous chemical reactions are incorporated. The importance of porous medium is suggested by using the Darcy–Forchheimer expressions. Moreover, the slip effects are incorporated over double rotating disk. The problem is formulated in terms of differential expressions. The analytical procedure is adopted via homotopic procedure. The accuracy of results is confirmed. Moreover, a optimized model for Artificial neural network (ANN) is developed as a novelty. The insight dynamic of physical parameters is assessed with aims of several graphs. The entropy generation pattern and evaluation of Bejan number is predicted due to flow parameters. The graphical simulations worked out form current model reveal that the entropy generation rate improves with Weissenberg number as well as slip factor. The presence of higher order slip is also effective to enhance the Bejan number.

In this article, a wavelet collocation method based on linear Legendre multi-wavelets is proposed for the numerical solution of the first as well as higher orders Fredholm, Volterra and Volterra–Fredholm integro-differential equations. The presented numerical method has the capability to tackle the solutions of both linear and nonlinear problems of these model equations. In order to endorse accuracy and efficiency of the method, it is tested on various numerical problems from literature with the aid of maximum absolute errors and rates of convergence. L ∞ norms are used to compare the numerical results with other available methods such as Multi-Scale-Galerkin’s method, Haar wavelet collocation method and Meshless method from literature. The comparability of the presented method with other existing numerical methods demonstrates superior efficiency and accuracy.

To obtain an accurate rotor position is an important part of sensorless control of permanent magnetic synchronous machine (PMSM) since PMSM is usually operated under speed varying conditions. However, the existing methods cannot provide a satisfactory tracking performance under harmonic polluted condition in wide operating range, which degrade the position detecting accuracy. In this paper, a recurrent neural network (RNN) based phase detection method is used for rotor position estimation of PMSM. To tackle the nonlinear problem in wide operating range of PMSM, RNN is used as a nonlinear dynamic system to establish the mapping relationship of the voltages of stator and rotor position. The proposed method can also provide frequency-adaptive filtering capability to remove the affect of harmonic. To validate the method, a comparison simulations with conventional SRF-PLL method are carried out under speed varying and harmonic disturbances conditions. The results confirm the effectiveness of the proposed method.

The flow through saturated porous soil is described by Darcy equation that generally has no analytical solution. Therefore, we have to use numerical methods to solve it. There exist several numerical methods and the well-known most used one is the finite elements method. In this work, we use a Diamond finite volumes scheme characterized with its conservation property to simulate Darcy equation in the linear and the non linear case in two dimensional case, based on permeability tensor. Different test cases are studied to validate the accuracy and the efficiency of the numerical model. The numerical scheme proves, through the obtained results, high level of accuracy comparing with the exact solution. The diamond finite volumes scheme for its ability to ensure the mass conservation of our model, knowing that the finite elements or the finite differences methods are less efficient on this side, our finite volumes method is the most suited to the Darcy flow and more faithful to physical problems comparing to other methods. We focused in our study on different aspects of the finite volumes scheme, the mass conservation, the non-linearity of the hydraulic conductivity and their interaction with the finite volumes method.

A novel nonlinear fractional order damped Pantographs equation involving input delay is formulated. We explored the controllability of the underlying nonlinear damped dynamical Pantograph equation of fractional order with input delay. The solution of the problem under consideration has initially expressed in the form of the Mittag–Leffler function in two different domains. The controllability Grammians matrices for both cases have been defined. Controllability in the linear case has been shown and applied Schaefer’s fixed point theorem as well as the Arzela-Ascoli theorem to derive necessary conditions for the controllability of the nonlinear case.

The point of this paper is to analyze and investigate the analytic-approximate solutions for fractional system of Volterra integro-differential equations in framework of Caputo-Fabrizio operator. The methodology relies on creating the reproducing kernel functions to gain analytical solutions in a uniform form of a rapidly convergent series in the Hilbert space. Using the Gram-Schmidt orthonomalization process, the orthonormal basis system is constructed in a dense compact domain to encompass the Fourier series expansion in view of reproducing kernel properties. Besides, convergence and error analysis of the proposed technique are discussed. For this purpose, several numerical examples are tested to demonstrate the great feasibility and efficiency of the present method and to support theoretical aspect as well. From a numerical point of view, the acquired solutions simulation indicates that the methodology used is sound, straightforward, and appropriate to deal with many physical issues in light of Caputo-Fabrizio derivatives.

Kinetic modeling plays a key role in development of large-scale extraction processes. In this study, we modeled the process of extracting essential oils from pomelo (Citrus maxima) peel materials in different kinetics including pseudo first order and pseudo second order kinetic models in both linear and nonlinear forms. The coefficient of determination, R2, and the percentage of deviation, %q, were used as the basis to determine the most suitable kinetic model kinetics. The results show that non-linear pseudo first order model (equation 7) was best fitted to describe the experimental data. The obtained essential oil was characterized by the abundance of limonene.

In this study, a stochastic differential equation capable of describing (using the motion function) the automatic manufacturing process of a lithium battery with a sleeve shell is introduced. The boundary-condition modeling method for this type of motion is an ordinary differential equation. The nonlinear equation is found using a dynamic method. The equations of the motions for the assembly process are derived by reducing the order of terms and separating the variables. Both the derivatives and integrals of the motion functions are derived and applied to describe the assembly process for a lithium battery. By using a characteristic constitutive assembly model, a new method to calculate the nonlinear terms is proposed. The main advantage of this method is that it can simplify the problem, which is done by finding the algebraic error in the region space of the motion function. The reliability and the applicability of the method were confirmed using a real-life example. Finally, by solving and improving the Euler model, the fourth-order Kutta method and Taylor series are applied to verify the correctness of the algorithm, and the convergence order of the function and the optimization of the assembly model are discussed. Through a one-dimensional search of the convergence domain, a method is found to make the analytical solution approximate the exact solution and reduce the calculation cost. This method in dynamics and mathematical engineering.

In this article, we presented a nonlinear time-fractional mathematical model of the Ebola Virus in order to understand the outbreak of this epidemic disease. Ebola virus is a highly contagious disease that can be spread in the population depending upon the number of individuals and their dynamics in the community. The Caputo and Atangana Baleanu fractional derivative operators are employed to get the solution of the system of fractional differential equations. The qualitative analysis has been made for the fractional-order model. Fixed-point theorem and an iterative schemes are used to get the existence and uniqueness. The actual behavior of the time-fractional model has been obtained by employing Laplace Adomian Decomposition technique. Finally, numerical results have been established for the system of fractional differential equations with simulations to demonstrate the impacts of the fractional-order parameters on the proposed system to achieve the theoretical outcomes and a comparison has been made with the Caputo for better analysis.

In the present study, the uniform cubic B-spline collocation method is constructed, employed, and experimented to given smooth approximations for the numerical solution of a class of linear and nonlinear fractional initial value problems of singular and non-singular types based on the conformable fractional derivative. As a special case, the singular Lane-Emden type model is presented such that the source fractional differential equation is transformed at the point of singularity. The converted issue is then solved by using third B-splines on a uniform mesh approximation procedure with help of Mathematica 11. Several illustrative examples are incorporated to demonstrate the efficiency, validity, and applicability of the proposed technique for such conformable problems.

The absence of satisfactory results that address the stability analysis of nonlinear incommensurate Fractional-order Difference Systems (FoDSs) as well as the impossibility of establishing a proper Lyapunov function that helps us to reveal any stability outcome for those systems, are considered some significant nonlinear problems that should be taken into account. To overcome such dilemmas, the present work provides some novel convenient conditions that can be utilized to ensure the asymptotic stability of those systems. In particular, through utilizing some features of the Z-transform scheme, we intend to propose certain results that aim to reveal the stability of the nonlinear incommensurate fractional-order difference system formulated in the sense of the Caputo difference operator. These novel results are completely confirmed by demonstrating the stability of the numerical solutions for two nonlinear difference systems with incommensurate fractional-orders.

In-depth convergence analyses for neutronics/thermal-hydraulics (T/H) coupled calculations are performed to investigate the performance of nonlinear methods based on the Fixed-Point Iteration (FPI). A simplified neutronics-T/H coupled system consisting of a single fuel pin is derived to provide a testbed. The xenon equilibrium model is considered to investigate its impact during the nonlinear iteration. A problem set is organized to have a thousand different fuel temperature coefficients (FTC) and moderator temperature coefficients (MTC). The problem set is solved by the Jacobi and Gauss-Seidel (G-S) type FPI. The relaxation scheme and the Anderson acceleration are applied to improve the convergence rate of FPI. The performances of solution schemes are evaluated by comparing the number of iterations and the error reduction behavior. From those numerical investigations, it is demonstrated that the number of FPIs is increased as the feedback is stronger regardless of its sign. In addition, the Jacobi type FPIs generally shows a slower convergence rate than the G-S type FPI. It also turns out that the xenon equilibrium model can cause numerical instability for certain conditions. Lastly, it is figured out that the Anderson acceleration can effectively improve the convergence behaviors of FPI, compared to the conventional relaxation scheme.

The current non-homogeneous nanofluid flow model is carried out to scrutinize the performance of the generalized Fourier's and Fick's laws on the MHD bioconvective aspects of couple-stress nanofluid flows through a convectively heated stretching sheet in the presence of activation energy and multiple stratified boundary conditions. Herein, both the concentrations of solid nanoparticles and motile microorganisms are incorporated explicitly into the nonlinear differential expressions describing the present non-Newtonian nanofluid flow model. Besides, the combined thermal influence of the Cattaneo-Christov heat flux and thermal radiation are also discussed. From a practical point of view, the couple-stress nanofluids are useful for examining different types of thermophysical and rheological features, since this kind of enhanced fluids can clarify realistically the dynamical behavior of various liquids, like the human blood and some polymeric suspensions. For reducing the mathematical complexity of the present physical problem, several effective similarity transformations are introduced formally to simplify the resulting partial differential equations (PDEs) into a nonlinear coupled structure of ordinary differential equations (ODEs). Moreover, the transformed dimensionless self-similarity equations are then numerically solved using the built-in shooting technique with the aid of the bvp4c solver MATLAB package. Furthermore, The obtained results are authenticated with an outstanding agreement. In this respect, the engineering quantities of interest are computed extensively with a higher level of accuracy and then summarized tabularly. To illustrate the impacts of the embedded physical parameters on the profiles of velocity, temperature, nanoparticles concentration, and microorganisms concentration, various illustrations are done successfully along with detailed elucidations. As the main findings, it is found that the temperature distribution and the microorganisms concentration profile can be enhanced with the higher values of the bioconvection Rayleigh number. Similarly, it is revealed that the nanoparticles concentration sketch and the microorganisms concentration profile can be boosted up for the higher magnitudes of the buoyancy ratio parameter.

As a valid numerical method to obtain a high-resolution result of a flow field, computational fluid dynamics (CFD) have been widely used to study coolant flow and heat transfer characteristics in fuel rod bundles. However, the time-consuming, iterative calculation of Navier-Stokes equations makes CFD unsuitable for the scenarios that require efficient simulation such as sensitivity analysis and uncertainty quantification. To solve this problem, a reduced-order model (ROM) based on proper orthogonal decomposition (POD) and machine learning (ML) is proposed to simulate the flow field efficiently. Firstly, a validated CFD model to output the flow field data set of the rod bundle is established. Secondly, based on the POD method, the modes and corresponding coefficients of the flow field were extracted. Then, an deep feed-forward neural network, due to its efficiency in approximating arbitrary functions and its ability to handle high-dimensional and strong nonlinear problems, is selected to build a model that maps the non-linear relationship between the mode coefficients and the boundary conditions. A trained surrogate model for modes coefficients prediction is obtained after a certain number of training iterations. Finally, the flow field is reconstructed by combining the product of the POD basis and coefficients. Based on the test dataset, an evaluation of the ROM is carried out. The evaluation results show that the proposed POD-ROM accurately describe the flow status of the fluid field in rod bundles with high resolution in only a few milliseconds.

In this work, we examine a nonlinear partial differential equation of fluid mechanics, namely, the generalized nonlinear advection–diffusion equation, which portrays the motion of buoyancy driven plume in a bent-on porous medium. Firstly, we classify all (point) symmetries of the equation, which prompt three cases of n. Next, for each case, we construct an optimal system of one-dimensional subalgebras and use them to perform symmetry reductions and symmetry invariant solutions. In a bid to explain the physical significance of some invariant solutions secured, we present a graphic display of some solutions in 3D, 2D as well as density plots via the exploitation of numerical simulations. Besides, we categorically state here that the results obtained in this study are new when compared with the outcomes previously achieved by Loubens et al., 2011 Quart. Appl. Math. 69 389–401. Interestingly, kink shape soliton, dark soliton, singular soliton together with exponential function solution wave profiles are displayed to make this work more valuable. Furthermore, we determine the conserved vectors in two different ways: engaging the general multiplier approach and Ibragimov’s conservation law theorem. Finally, we provide the physical meaning of these conservation laws.

Nonlinear optical materials, whose optical properties such as refractive index can be changed by light, are essential for advanced light functionalities such as all optical switching. In this chapter, the fundamentals of nonlinear optics have been described and the second- and third-order nonlinear optical materials based on both organic and inorganic molecules have been reviewed. In particular, the nonlinear optically active subwavelength scale architectures have been highlighted.

This chapter discusses systems of ordinary differential equations. It presents a review of matrix algebra and calculus. It defines the characteristic equation and characteristic polynomial and shows how to calculate characteristic polynomial and eigenvalues of matrices through examples. Mathematica can compute both the characteristic polynomial and eigenvalues directly with the commands CharacteristicPolynomial and Eigenvalues. The chapter illustrates the homogeneous system of first-order linear differential equations. It provides solution of homogeneous linear systems with constant coefficients through some examples. It also discusses some theorems and terminology used in establishing the fundamentals of solving systems of differential equations. To apply variation of parameters, one first calculates a fundamental matrix for the associated homogeneous equation. In many cases, Laplace transforms can be used to solve a system of linear differential equations. The chapter illustrates the techniques needed to accomplish this with Mathematica through examples. It further explains nonlinear systems, linearization, and equilibrium points.

A novel and effective artificial neural network (ANN) optimized using differential evolution (DE) is first introduced to provide a robust and reliable forecasting of jet grouted column diameters. The proposed computational method adopts the DE algorithm to tackle the difficulties in the training and performance of neural networks and optimize the four quintessential hyper-parameters (i.e. the epoch size, the number of neurons in a hidden layer, the number of hidden layers, and the regularization parameter) that govern the neural network efficacy. This approach is further enhanced by a stochastic gradient optimization algorithm to allow ‘expensive’ computation efforts. The ANN-DE is first trained using a prepared jet grouting dataset, then verified and compared with the prevalent machine learning tools, i.e. neural networks and support vector machine (SVM). The results show that, the ANN-DE outperforms the existing methods for predicting the diameter of jet grouting columns since it well balances training efficiency and model performance. Specifically, the ANN-DE achieved root mean square error (RMSE) values of 0.90603 and 0.92813 for the training and testing phases, respectively. The corresponding values were 0.8905 and 0.9006 for the optimized ANN, then, 0.87569 and 0.89968 for the optimized SVM, respectively. The proposed paradigm is bound to be useful for solving various geotechnical engineering problems regardless of multi-dimension and nonlinearity.

The space–time fractional equal width (EW) and the space–time fractional generalized equal width (GEW) equations are two important models that represent nonlinear dispersive waves, namely, waves ensuing in the shallow water channel, 1-D wave generation ascending in the nonlinear dispersive medium estimation, cold plasma hydro-magnetic waves, chemical kinematics, electromagnetic interaction, etc. In this article, we search advanced and broad-spectrum wave solutions of the formerly indicated models in diverse families in conjunction with the Riemann-Liouville fractional derivative via the double ( G ′ / G , 1 / G )-expansion approach. The nonlinear fractional differential equations (NLFDEs) are transformed into ODEs by the composite function derivative and the chain rule putting together with the wave transformation. We acquire kink wave solution, multiple periodic solutions, single soliton solution, periodic wave solution and other types of soliton solutions by setting particular values of the embodied parameters. The suggested technique is functional, convenient, powerful, and computationally feasible to examine scores of NLFDEs.

In this paper, we implemented the Exp-function method and the extended tanh method to finds the analytical solutions of one of the important nonlinear partial differential equations with variable coefficients called the new (3 + 1)-dimensional Date-Jimbo-Kashiwara-Miwa with time-dependent coefficients. Moreover, we find the numerical solutions to that equation using the finite difference method. The results demonstrate the effectiveness and convenience of the used methods. Comparison between our results through some tables and graphs to illustrate the accuracy of the applied methods. We obtained the different types of solutions-like bright, dark, periodic, rational and singular periodic soliton solutions using the different values of constant parameters. The obtained exact solutions may be useful to understand the mechanism of the complicated nonlinear physical phenomena which are related to wave propagation in (3 + 1)-dimensional Date-Jimbo-Kashiwara-Miwa with time-dependent coefficients model.

In this paper, Crank-Nicolson differential quadrature method based on cubic exponential B-spline (CExpB-spline) functions is presented to approximate the 1D nonlinear hyperbolic Sine-Gordon equation (SGE). The time derivative is discretized by the usual forward difference scheme while the differential quadrature method (DQM) is used to integrate the spatial derivatives. The discretization of the problem gives systems of linear equations. Three numerical examples are chosen to investigate the efficiency and accuracy of the method. It is observed that the proposed method provides excellent results than the existing methods. The rate of convergence (ROC) of the present method is obtained numerically showing that the method is second-order accurate in space.

In this analysis, the modified nanofluid flow at a nonlinear stretching Riga plate is considered. The impacts of variable viscosity are considered. The modified nanofluid is the extended version of the hybrid nanofluid. This is the mixture of three nanoparticle and base fluid. The heat transfer rate depends on the thermal conductivity because heat transfer rate and thermal conductivity directly proportion which provided in the literature. The developed model solved through numerical technique. The basic achievement of this analysis is to explore about the heat transfer improvement that gains higher as compared to Hybrid nanofluid and nanofluid, (see Fig. 1 ). Heat transfer properties and modified nanofluid show exciting behavior which deserve further study on the modified nanofluid. The ϕ 3 disperse the energy in the shape of heat than the mixture of more nanoparticles may more exert energy in the form of heat.

In this paper, we study a fourth-order nonlinear symmetric regularized long-wave equation which arises in several physical applications including ion sound waves in plasma. This model also describes nonlinear ion-acoustic and space-charge waves. Lie group analysis and the tanh-coth method is utilized for the construction of solitary wave solutions to the equation. Based on each symmetry, we reduce the considered partial differential equation into different ordinary differential equations. The obtained equations are solved and new solitary wave patterns are reported. To understand the physical interpretation, some solitary wave structures are exhibited graphically. Also, by using the multiplier approach, we constructed the local conservation laws of the considered equation.

Oil price forecasting is one of the most challenging issues since it is noisy, non-stationary, and chaotic. In this paper, we design a Bayesian Nonlinear Quantile method consisting of a Threshold Improved model and an Adaptive MCMC model to improve predicting performance. Specifically, the threshold improve model is introduced to solve the problems caused by the completely asymmetric distribution, and the Adaptive MCMC model is used to get the optimal threshold. Besides, the two-stage framework is applied to improve traditional methods' performance, including the Indirect GARCH model and Asymmetric Slope model. The experimental results show that our approach provides a promising alternative to oil price prediction, and the framework also improve the performance of the traditional methods. The contribution of this paper is to improve the accuracy of the oil price forecasting model, and the framework applies to other energy prices as well.

In this new-fangled research, the mixed convective stagnation point flow of a hybrid nanofluid over a yawed cylinder with radiation impact is considered. In reality, the perception of mixed convection in the study of yawed cylinder rises in heat exchangers. To explore the heat diffusion through the system of mixed convection, the mathematical problem is formed in the form of partial differential equations which are coupled and nonlinear. A solution technique is applied and described for indulgencing non-similar thermal boundary layers. The non-similar terms involving in the transformed equations are held without approximations. The non-similar equations are solved numerically using the bvp4c technique. The exploration divulges numerous significant results involving yaw angle, hybrid nanoparticle volume fraction, mixed convection, radiation, and non-similarity phenomena. The impact of the yaw angle in enhancing the velocity of the hybrid nanofluid in the span-wise and chord-wise directions in the aiding buoyancy flow and decelerating in the opposing flow, while the contrary behavior is noticed for the dimensionless temperature profile. Also, the hybrid nanoparticles reduce the velocity in both directions in case of assisting as well as opposing flow, whereas the dimensionless temperature augments.

In this paper, we develop a least-squares support vector machine (LS-SVM) for solving a nonlinear fractional-order Volterra’s population model in a closed system. The fractional rational Legendre functions with an orthogonal property on a semi-infinite domain have been used as the kernel of LS-SVM. Learning the solution is done by solving a non-linear constrained optimization problem. To accelerate the learning process, we propose two different approaches based on the orthogonality of kernels and a shared-memory task parallelization scheme for multi-core systems. By carrying out several experiments, it is seen that the proposed approaches provide accurate solutions for fractional-order Volterra’s population model.

The electricity distribution in a planned way has been a difficult issue that the power supply bureau wishes to solve, and it is the lifeblood of economic development. Forecasting annual electricity consumption is very crucial for the planning of the power supply bureau and for booming economic development. We propose a novel unbiased fractional nonlinear grey Bernoulli model [i.e, UFNGBM (1,1)] to forecast China’s annual electricity consumption based on the nonlinear grey Bernoulli model [i.e, NGBM (1,1)]. First, UFNGBM (1,1) approach is designed to derive calculation formula of the novel model, and validity of the model is proved by the matrix perturbation theory. Second, a novel optimization algorithm is introduced based on the whale algorithm to find the optimal parameters (i.e., o r d e r and p o w e r ) of the proposed model. Third, the accuracy, stability, and effectiveness of our method are verified through three real-world cases in China. Finally, we collect the electricity consumption data of three provinces in China and successfully apply the proposed algorithm to predict the electricity consumption from 2019 to 2024. The experimental results demonstrate that our proposed model is significantly superior to nine alternative models on the electricity consumption data of Jilin and Jiangsu. The performance of our novel method is close to the state-of-the-art deep learning method on the electricity consumption data of Shandong. It is noticed that our method [as an extended version of NGBM(1,1)] is significantly better than NGBM(1,1) on these three real-world datasets, which further shows the effectiveness of the our proposed algorithm. Meanwhile, the electricity consumption of these three provinces in the next six years (2019–2024) is forecasted, which has a very good guiding significance and provides a more reliable reference for the economic and power bureau.

Due to the enormous demand of various industries for crude oil and its compositions, petroleum and drilling industries have always tried to find novel solutions, especially in drilling operations, to virtually eliminate the operational costs. Mechanical specific energy (MSE) is the required energy in underground formations to drill the rock formations, which should be analyzed parametrically to estimate drilling inefficiencies correctly. It has caused to improve the drilling operations and effectiveness of drilling bite lifetime. Using SPSS-Ver023 software as an appropriate statistical and analytical model, the drilling bit rate of penetration (ROP) was optimized. Then, the drilling parameters such as weight on bit (WOB) was optimized as the energy-efficient parameter in MSE design. Data gathering was collected from three underground formations to derive linear and non-linear correlations from having a proper analysis. It allows us to have an accurate analysis of the appropriateness of derived correlations. It is concluded that non-linear correlations would provide accurate results as it is derived by more sensitive data and can be extended to similar formations in the specific area.

Deriving optimal photovoltaic (PV) models’ optimal parameters have tremendous significance in simulating, evaluating, and controlling the photovoltaic systems. Determining unknown parameters of these PV models is a multimodal, nonlinear, and complex optimization problem. Hence, developing a robust optimization model to achieve optimal parameters of the PV models effectively is essential. This paper proposes an enhanced metaphor-free gradient-based optimizer (EGBO) for extracting PV parameters quickly, precisely, and reliably. In the EGBO, a rank-based mechanism is employed to update its parameters efficiently. Also, the logistic map (LC) is implemented to better use the local escaping operator (LEO) in the original GBO algorithm. The proposed EGBO optimally identifies various parameters in the PV model, such as single diodes, double diodes, and PV modules. The relevant results indicate that compared with most advanced optimization methods, the EGBO algorithm is competitive in reliability, accuracy, and convergence speed. Moreover, the relevant results from the experimental data drawn from the manufacturer’s datasheet demonstrate that the developed approach can offer highly accurate solutions at various irradiances and temperatures. Consequently, the achieved results confirm that the novel approach can be presented as a utility tool for deriving optimal PV models’ optimal parameters, and it can be helpful in modeling PV systems.

Developing an accurate mathematical model is an essential tool for studying and optimizing the performance of the photovoltaic cell system (PV). Transforming the PV problem into an optimization problem in which meta-heuristic algorithms excel provides an alternative approach to identifying the PV model’s parameters. The memetic evolution mechanism and the shuffling strategy included in the shuffling frog-leaping algorithm (SFLA) provide safeguards for solving nonlinear, multimodal, and high-dimensional problems. However, the low convergence accuracy is an essential drawback of the SFLA algorithm to solve the PV problem. This paper proposes a delayed dynamic step mechanism based on the SFLA algorithm’s characteristics to overcome this disadvantage, called the DDSFLA algorithm. The results of testing 23 benchmark functions and extracting the single diode model, the double-diode model, and the PV module show that the DDSFLA algorithm has a faster convergence speed and higher convergence accuracy and exhibits strong optimization stability under the special conditions of different temperatures or light intensities. The results suggest that the proposed algorithm can be used as an effective method to handle PV models’ parameter extraction. The extra resources and online user guidance for this research will be provided at https://aliasgharheidari.com .

A deep learned recurrent type-3 (RT3) fuzzy logic system (FLS) with nonlinear consequent part is presented for renewable energy modeling and prediction. Beside the rule parameters, the values of horizontal slices and membership function (MF) parameters are also optimized. The stability of suggested learning scheme is guaranteed. The proposed method is applied for modeling of both solar panels and wind turbines. By the use of experimental setup and generated real-world date sets, the applicability of suggested approach is shown. Comparison with convectional FLSs demonstrates the superiority of the suggested scheme.

Waveform inversion is an approach used to find an optimal model for the velocity field of a ground structure such that the dynamic response is close enough to the given seismic data. First, a suitable numerical approach is employed to establish a realistic forward computer model. The forward problem is solved in the frequency domain using higher-order finite elements. The velocity field is inverted over a specific number of discrete frequencies; thereby, reducing the computational cost of the forward calculation and the nonlinearity of the inverse problem. The results are presented for different frequency sets and with different source and receiver locations for a two-dimensional model. The influence of attenuation effects is also investigated. The results of two blind tests are presented where only the seismic records of an unknown synthetic model with an inhomogeneous material parameter distribution are provided to mimic a more realistic case. Finally, the result of the inversion in a three-dimensional space is illustrated.

The multiple-order line rogue wave solutions method is emp loyed for searching the multiple soliton solutions for the generalized (2 + 1)-dimensional Camassa-Holm-Kadomtsev-Petviashvili (CHKP) equation, which contains first-order, second-order, and third-order waves solutions. At the critical point, the second-order derivative and Hessian matrix for only one point will be investigated and the lump solution has one minimum value. For the case, the lump solution will be shown the bright-dark lump structure and for another case can be present the dark lump structure-two small peaks and one deep hole. Also, the interaction of lump with periodic waves and the interaction between lump and soliton can be obtained by introducing the Hirota forms. In the meanwhile, the cross-kink wave and periodic wave solutions can be gained by the Hirota operator. The physical phenomena of these gained multiple soliton solutions are analyzed and indicated in figures by selecting suitable values. We alternative offer that the determining method is general, impressive, outspoken, and powerful and can be exerted to create exact solutions of various kinds of nonlinear models originated in mathematical physics and engineering.

Numerical modeling for the safety-related equipment used in a nuclear power plant (i.e., cabinet facilities) plays an essential role in seismic risk assessment. A full finite element model is often time-consuming for nonlinear time history analysis due to its computational modeling complexity. Thus, this study aims to generate a simplified model that can capture the nonlinear behavior of the electrical cabinet. Accordingly, the distributed plasticity approach was utilized to examine the stiffness-degradation effect caused by the local buckling of the structure. The inherent dynamic characteristics of the numerical model were validated against the experimental test. The outcomes indicate that the proposed model can adequately represent the significant behavior of the structure, and it is preferred in practice to perform the nonlinear analysis of the cabinet. Further investigations were carried out to evaluate the seismic behavior of the cabinet under the influence of the constitutive law of material models. Three available models in OpenSees (i.e., linear, bilinear, and Giuffre-Menegotto-Pinto (GMP) model) were considered to provide an enhanced understating of the seismic responses of the cabinet. It was found that the material nonlinearity, which is the function of its smoothness, is the most effective parameter for the structural analysis of the cabinet. Also, it showed that implementing nonlinear models reduces the seismic response of the cabinet considerably in comparison with the linear model.

To develop, redesign, and enforce prudent energy policies, investigating the causality between waste-to-energy and energy consumption is beneficial for policymakers. Although there are several studies on this topic, there is no consistent conclusion. Hence, this study employs the linear and nonlinear Granger causality tests to detect the bi-directional causality between waste-to-energy and energy consumption in both producer and consumer sides. The results show a bi-directional linear causal relationship between the waste-to-energy and energy consumption in industry, indicating sustainable waste management in German industries. Moreover, we find evidence of the uni-directional nonlinear causal relationship running from waste-to-energy to energy net imports, confirming the existence of the nonlinear effect of waste-to-energy on Germany’s net energy imports.

In this paper, we find the solutions for fractional potential Korteweg–de Vries (p-KdV) and Benjamin equations using q -homotopy analysis transform method ( q -HATM ) . The considered method is the mixture of q -homotopy analysis method and Laplace transform, and the Caputo fractional operator is considered in the present investigation. The projected solution procedure manipulates and controls the obtained results in a large admissible domain. Further, it offers a simple algorithm to adjust the convergence province of the obtained solution. To validate the q -HATM is accurate and reliable, the numerical simulations have been conducted for both equations and the outcomes are revealed through the plots and tables. Comparison between the obtained solutions with the exact solutions exhibits that, the considered method is efficient and effective in solving nonlinear problems associated with science and technology.

In the real world, the demands for some specific goods may increase in some special occasions. At such conditions, in-time delivery of the desired goods and minimization of the traveling costs will be found crucial importance for the customers and the suppliers, respectively. In this paper, a new mathematical model consisting of two objectives: minimizing traveling costs and maximizing customers’ demand satisfaction was proposed through a multi-objective optimization approach. The nonlinear equations were converted to linear equations and the proposed model was then solved using CPLEX solver by GAMS23.6.3 software. Two approaches were proposed to solve the problem based on the NSGA-II algorithm with different modifications in the mutation operator. A two-row structure was also employed for the chromosomes. This research contributes to vehicle routing literature considering time windows, multiple demands, and two conflict objectives and proposes two metaheuristic algorithms. The algorithm results were also compared with two criteria: covered non-dominated solutions and spread solutions. The results show that the improvements were made with the variation in the mutation operator in both criteria. In summary, the developed vehicle routing mathematical model works effectively for some real-world logistic problems with occasional goods, and the customer satisfaction in due time is incorporated in the mathematical model.