Article
Mathematics, Applied
R. Katani, S. McKee
Summary: Various numerical methods have been proposed for solving weakly singular Volterra integral equations, but this paper focuses on a method for solving two-dimensional nonlinear weakly singular Volterra integral equations of the second kind. By applying a simple smoothing change of variables and employing Navot's quadrature rule, the transformed integral equation is solved with smooth solutions. Theoretical results are verified through numerical examples.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Zexiong Zhao, Chengming Huang
Summary: This paper focuses on the numerical solution of Volterra integro-differential equations with weakly singular kernels. A smoothing transformation is applied to improve the regularity of the original equation. The collocation method based on barycentric rational interpolation is introduced and the convergence and superconvergence of the numerical solution are analyzed. Numerical results are presented to validate the theoretical predictions of convergence and superconvergence.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Computer Science, Interdisciplinary Applications
Mahmoud A. Zaky, Ibrahem G. Ameen
Summary: This work presents a spectrally accurate collocation method for solving weakly singular integral equations in high dimensions, utilizing multivariate Jacobi approximation and smoothing transformation to address singularity issues. Rigorous convergence analysis and numerical tests were conducted, confirming the effectiveness of the proposed method for nonsmooth solutions in two dimensions. The results provide a theoretical justification for high-dimensional nonlinear weakly singular Volterra type equations with nonsmooth solutions.
ENGINEERING WITH COMPUTERS
(2021)
Article
Mathematics, Applied
Xiaohua Ma, Chengming Huang
Summary: This paper rigorously analyzes the exponential convergence of the Chebyshev collocation method for third kind linear Volterra integral equations, utilizing a smoothing transformation to overcome singularity issues at the beginning of time. The numerical method achieves spectral accuracy and is demonstrated to be applicable and efficient through examples with non-smooth solutions.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Yifei Wang, Jin Huang, Li Zhang, Ting Deng
Summary: In this paper, an efficient approach for solving multi-dimensional systems of weakly singular Volterra integral equations (SVIEs) is proposed. Smooth transformations are used to convert the original equation into a new equation with a smoother solution. Euler polynomials combined with Gauss-Jacobi quadrature formula are used to efficiently solve the transformed equation, and the numerical solution of the original equation is obtained through inverse transformations. The existence and uniqueness of the solution are proved, and the convergence analysis and error estimate of the proposed method are given.
NUMERICAL ALGORITHMS
(2022)
Article
Mathematics, Applied
Zheng Ma, Anatoly A. Alikhanov, Chengming Huang, Guoyu Zhang
Summary: This paper introduces a multi-domain Muntz-polynomial spectral collocation method with graded meshes for solving second kind Volterra integral equations with a weakly singular kernel, particularly suitable for problems with non-integer exponent factors in the solutions. A rigorous error analysis of hp-version in the L-infinity- and weighted L-2-norms is carried out, and several numerical examples are presented to demonstrate the efficiency and accuracy of the method.
APPLIED NUMERICAL MATHEMATICS
(2021)
Article
Mathematics, Applied
Sayed Arsalan Sajjadi, Saeed Pishbin
Summary: This paper investigates a product integration method based on orthogonal polynomials for solving mixed systems of Volterra integral equations with weakly singular kernels. Theoretical and numerical analysis, including tractability index and nu-smoothing property extension, are conducted for the mixed systems. Convergence analysis of the method is derived, and two examples are provided to illustrate the theoretical error estimation.
NUMERICAL ALGORITHMS
(2021)
Article
Mathematics, Applied
Chuanli Wang, Biyun Chen
Summary: We propose a multi-step spectral collocation method for solving Caputo-type fractional integro-differential equations with weakly singular kernels. By reformulating the problem as a second type Volterra integral equation with two different weakly singular kernels, we construct a multi-step Legendre-Gauss spectral collocation scheme and rigorously establish the hp-version convergence. Numerical experiments are conducted to validate the effectiveness of the suggested method and the theoretical results.
Article
Engineering, Electrical & Electronic
Ming-Da Zhu, Tapan K. Sarkar, Yu Zhang
Summary: This article discusses the relationship between near-singularity and shape-dependence of singularity cancellation schemes, and presents a novel framework for calculating weakly near-singular integrals in both regular and irregular triangular domains, demonstrating the effectiveness of the theoretical framework and efficiency of the proposed transformations through numerical results.
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION
(2021)
Article
Mathematics, Applied
Moumita Mandal, Kapil Kant, Gnaneshwar Nelakanti
Summary: This article studies the discrete versions of Legendre spectral and iterated Legendre spectral techniques for solving second kind Hammerstein type weakly singular integral equations, achieving convergence analysis and orders using numerical quadrature rules. Numerical aspects are provided to verify the hypothetical results.
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
(2021)
Article
Mathematics, Applied
Qiumei Huang, Min Wang
Summary: This paper discusses the superconvergence of interpolated collocation solutions for weakly singular Volterra integral equations of the second kind. It introduces two different interpolation postprocessing approximations for higher accuracy and demonstrates their efficiency through numerical experiments.
COMPUTATIONAL & APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Jiashu Lu, Mengna Yang, Yufeng Nie
Summary: This paper considers efficient spectral solutions for weakly singular nonlocal diffusion equations with Dirichlet-type volume constraints. The proposed method utilizes two-sided Jacobi spectral quadrature rules for approximating the integral operator and presents a rigorous convergence analysis with the L-infinity norm. It is further proven that the Jacobi collocation solution converges to its corresponding local limit as nonlocal interactions vanish. Numerical examples are provided to verify the theoretical results.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Engineering, Multidisciplinary
I. G. Ameen, N. A. Elkot, M. A. Zaky, A. S. Hendy, E. H. Doha
Summary: This study aims to numerically solve a class of nonlinear fractional two-point boundary value problems by recasting the problem into an equivalent system of weakly singular integral equations and using a Legendre-based spectral collocation method. The method's construction and analysis are presented, and its applicability to fractional optimal control problems is indirectly shown through Euler-Lagrange equations. Numerical examples confirm the convergence and robustness of the scheme.
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES
(2021)
Article
Mathematics, Applied
Mahmoud A. Zaky, Ibrahem G. Ameen, Nermeen A. Elkot, Eid H. Doha
Summary: This paper introduces a spectral collocation method for solving a general class of nonlinear systems of multi-dimensional integral equations. The method uses Legendre spectral quadrature rule to approximate integral terms for high-order accuracy, and establishes the spectral rate of convergence in the L-2-norm, showing exponential decay of error in the approximate solution. Numerical examples validate the theoretical prediction.
APPLIED NUMERICAL MATHEMATICS
(2021)
Article
Mathematics, Applied
Walid Remili, Azedine Rahmoune, Chenkuan Li
Summary: This paper investigates the Galerkin spectral method for solving linear second-kind Volterra integral equations with weakly singular kernels on large intervals. By using variable substitutions, the equation is transformed into an equivalent semi-infinite integral equation with nonsingular kernel, allowing the inner products from the Galerkin procedure to be evaluated using Gaussian quadrature. The error analysis based on the Gamma function demonstrates the spectral rate of convergence, and several numerical experiments are conducted to validate the theoretical results.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Engineering, Multidisciplinary
Ahmed S. Hendy, Mahmoud A. Zaky, Eid H. Doha
Summary: The aim of this paper is to derive a novel discrete form of stochastic fractional Gronwall lemma involving a martingale. The proof of the derived inequality is accomplished by a corresponding no randomness form of the discrete fractional Gronwall inequality and an upper bound for discrete-time martingales representing the supremum in terms of the infimum. The main challenges of the stated and proved main theorem are the release of a martingale term on the right-hand side of the given inequality and the graded L1 difference formula for the time Caputo fractional derivative of order 0 < alpha < 1 on the left-hand side. An a priori estimate for a discrete stochastic fractional model is derived using the constructed theorem.
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
(2023)
Article
Mathematics, Applied
Dina Mostafa, Mahmoud A. Zaky, Ramy M. Hafez, Ahmed S. Hendy, Mohamed A. Abdelkawy, Ahmed A. Aldraiweesh
Summary: We introduce a class of orthogonal functions based on Jacobi polynomials, generated by applying a tanh transformation. Interpolation and projection error estimates are constructed using weighted pseudo-derivatives tailored to the mapping. Then, we develop an efficient spectral tanh Jacobi collocation method for the numerical simulation of nonlinear Schrodinger equations on the infinite domain using the nodes of the newly introduced tanh Jacobi functions.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics
K. Van Bockstal, A. S. Hendy, M. A. Zaky
Summary: This work focuses on investigating the initial-boundary value problem for a fractional wave equation with space-dependent variable-order and coefficients that depend on both spatial and time variables. This type of operator is commonly used in the modeling of viscoelastic materials. The global existence of a unique weak solution to the model problem has been proven under appropriate data conditions, using Rothe's time discretization method.
QUAESTIONES MATHEMATICAE
(2023)
Article
Mathematics, Applied
Hao Chen, Wenlin Qiu, Mahmoud A. Zaky, Ahmed S. Hendy
Summary: A two-grid temporal second-order scheme is proposed to solve the two-dimensional nonlinear Volterra integro-differential equation with a weakly singular kernel. The scheme aims to reduce computation time and improve the accuracy compared to the previous scheme developed by Xu et al. The proposed scheme involves solving a small nonlinear system on a coarse grid, using Lagrange's linear interpolation formula to obtain auxiliary values for the fine grid analysis, and solving a linearized Crank-Nicolson finite difference system on the fine grid. The algorithm utilizes central difference approximation for spatial derivatives and Crank-Nicolson technique and product integral rule for approximating the temporal derivative and integral term, respectively. The proposed approach is proven to have stability and space-time second-order convergence using the discrete energy method in L-2-norm. Numerical verification demonstrates the effectiveness of the algorithm through agreement between numerical results and theoretical analysis.
Article
Engineering, Mechanical
Ahmed S. Hendy, Mahmoud A. Zaky, Karel Van Bockstal
Summary: In this paper, we investigate the longtime behavior of time fractional reaction-diffusion equations with delay. Energy estimates, asymptotic stability, and asymptotic contractivity of the problem are proved. Numerical experiments are performed to confirm the findings.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics, Applied
R. Wang, L. Qiao, M. A. Zaky, A. S. Hendy
Summary: In this paper, a numerical solution for the nonlinear tempered fractional integrodifferential equation in three dimensions is provided. The trapezoidal convolution rule with backward differences (BDF2) is used for temporal discretization, and an alternating direction implicit difference scheme is developed for spatial discretization. A novel fast approximation method is applied to handle the nonlinear term. The stability and convergence analysis of the numerical scheme are performed, and numerical experiments are conducted to validate the theoretical results.
NUMERICAL ALGORITHMS
(2023)
Article
Mathematics, Applied
Hamed Ould Sidi, Mahmoud A. Zaky, Wenlin Qiu, Ahmed S. Hendy
Summary: This study focuses on the reconstruction of an unknown source function for hyperbolic partial differential equations with interior degeneracy. The spatial element of the source term in a degenerate wave equation is determined using final observation data. The existence and uniqueness of the direct problem with interior degeneracy within the spatial domain are established and proven. The inverse problem is formulated as a nonlinear optimization problem, where the unknown source term is characterized as the solution to a minimization problem.
APPLIED NUMERICAL MATHEMATICS
(2023)
Article
Mathematics, Applied
Meihui Zhang, Jinhong Jia, Ahmed S. Hendy, Mahmoud A. Zaky, Xiangcheng Zheng
Summary: We propose a fast numerical technique for a time-fractional option pricing model with asset-price-dependent variable order. The method can handle the complicated variable-order fractional derivative and its fast approximations and overcomes the uncommon difficulties caused by the coupled temporal coefficients and the loss of monotonicity. We demonstrate that the proposed method has error estimates and significantly reduces the computational cost compared to the traditional time-stepping solver.
APPLIED NUMERICAL MATHEMATICS
(2023)
Article
Mathematics, Applied
Karel Van Bockstal, Mahmoud A. Zaky, Ahmed Hendy
Summary: In this study, a wave equation with a time-dependent variable-order fractional damping term and a nonlinear source is investigated. The existence and uniqueness of the problem are explored using Rothe's method, avoiding the need for closed-form expressions in terms of special functions. A weak formulation is proposed, and the uniqueness of the solution is established using Gronwall's lemma. A uniform mesh time-discrete scheme is introduced based on a backward discrete convolution approximation, and a priori estimates are obtained for the time-discrete solution. The full discretisation of the problem is achieved using Galerkin spectral techniques, and numerical examples are provided.
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
(2023)
Article
Mathematics
Ebrahim Amini, Mojtaba Fardi, Mahmoud A. Zaky, Antonio M. Lopes, Ahmed S. Hendy
Summary: In this paper, a differential operator is defined on an open unit disk &UDelta; using the BD operator and convolution. New subclasses of p-valent functions are introduced using the principle of differential subordination, and inclusion relations between these classes are studied. Results related to analytic functions and analytic univalent functions are derived, providing insights for developing p-univalent functions and further research in complex analysis.
Article
Mathematics
Hamed Ould Sidi, Mahmoud A. Zaky, Rob H. De Staelen, Ahmed S. Hendy
Summary: This paper focuses on the simultaneous reconstruction of the initial condition and the space-dependent reaction coefficient in a multidimensional hyperbolic partial differential equation with interior degeneracy. It proposes a reconstruction scheme using temporal integral observation. The well-posedness, existence, and uniqueness of the inverse problem are discussed, and the problem is reformulated as a least squares minimization problem, with the Frechet gradients determined using the adjoint and sensitivity problems. An iterative construction procedure is developed using the conjugate gradient algorithm and the discrepancy principle as a stopping criterion. Numerical experiments are conducted to validate the performance of the reconstruction scheme in one and two dimensions.
Article
Mathematics, Interdisciplinary Applications
Mohammadhossein Derakhshan, Ahmed S. Hendy, Antonio M. Lopes, Alexandra Galhano, Mahmoud A. Zaky
Summary: In this paper, we propose a novel numerical scheme to solve the time-fractional advection-dispersion equation with distributed-order Riesz-space fractional derivatives. This method reformulates the distributed-order Riesz-space fractional derivatives by means of a second-order linear combination of Riesz-space fractional derivatives. The resulting equation is transformed into a time-fractional ordinary differential equation using the matrix transform technique, and a discretization method is used to approximate the weakly singular kernel. The stability, convergence, and error analysis are presented, and simulations are performed to verify the theoretical findings.
FRACTAL AND FRACTIONAL
(2023)
Article
Physics, Multidisciplinary
M. A. Zaky, A. S. Hendy, A. A. Aldraiweesh
Summary: A numerical simulation technique is developed in this paper for the coupled system of variable-order time fractional nonlinear Schr？dinger equations using the finite difference/spectral method. The proposed algorithm discretizes the variable-order Caputo time-fractional derivative using the finite difference method and uses the spectral technique for spatial approximation. The advantage of this algorithm is that it does not require an iterative procedure for the nonlinear term in the coupled system. Numerical experiments are performed to verify the accuracy of the method.
ROMANIAN REPORTS IN PHYSICS
(2023)
Article
Thermodynamics
H. Afsar, G. Peiwei, A. Alshamrani, M. M. Alam, A. S. Hendy, M. A. Zaky
Summary: This article explores the electroosmotic peristaltic flow in asymmetric channels using hybrid non-Newtonian nanofluids and emphasizes its significant potential in various domains such as microfluidics, electronics cooling, energy systems, and biomedical applications.
CASE STUDIES IN THERMAL ENGINEERING
(2023)
Article
Mathematics, Applied
Mahmoud A. Zaky, Ahmed S. Hendy, Jorge E. Macias-Diaz
Summary: This paper proposes and analyzes a high-order difference/Galerkin spectral scheme for the time-space fractional Ginzburg-Landau equation. The scheme achieves spectral accuracy in space and second-order accuracy in time. Error estimates are established using a fractional Gronwall inequality and its discrete form. Numerical experiments confirm the theoretical claims and discuss the effect of fractional-order parameters on pattern formation.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Applied
M. S. Bruzon, T. M. Garrido, R. de la Rosa
Summary: We study a family of generalized Zakharov-Kuznetsov modified equal width equations in (2+1)-dimensions involving an arbitrary function and three parameters. By using the Lie group theory, we classify the Lie point symmetries of these equations and obtain exact solutions. We also show that this family of equations admits local low-order multipliers and derive all local low-order conservation laws through the multiplier approach.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Dohee Jung, Changbum Chun
Summary: The paper presents a general approach to enhance the Pade iterations for computing the matrix sign function by selecting an arbitrary three-point family of methods based on weight functions. The approach leads to a multi-parameter family of iterations and allows for the discovery of new methods. Convergence and stability analysis as well as numerical experiments confirm the improved performance of the new methods.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Abhishek Yadav, Amit Setia, M. Thamban Nair
Summary: In this paper, we propose a Galerkin's residual-based numerical scheme for solving a system of Cauchy-type singular integral equations using Chebyshev polynomials. We prove the well-posedness of the system and derive a theoretical error bound and convergence order. The numerical examples validate the theoretical results.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Fernando Chacon-Gomez, M. Eugenia Cornejo, Jesus Medina, Eloisa Ramirez-Poussa
Summary: The use of decision rules allows for reliable extraction of information and inference of conclusions from relational databases, but the concepts of decision algorithms need to be extended in fuzzy environments.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Ilhame Amirali, Gabil M. Amiraliyev
Summary: This paper considers the one-dimensional initial-boundary problem for a pseudoparabolic equation with a time delay. To solve this problem numerically, a higher-order difference method is constructed and the error estimate for its solution is obtained. Based on the method of energy estimates, the fully discrete scheme is shown to be convergent of order four in space and of order two in time. The given numerical results illustrate the convergence and effectiveness of the numerical method.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Tong-tong Shang, Guo-ji Tang, Wen-sheng Jia
Summary: The goal of this paper is to investigate a class of linear complementarity problems over tensor-spaces, denoted by TLCP, which is an extension of the classical linear complementarity problem. First, two classes of structured tensors over tensor-spaces (i.e., T-R tensor and T-RO tensor) are introduced and some equivalent characterizations are discussed. Then, the lower bound and upper bound of the solutions in the sense of the infinity norm of the TLCP are obtained when the problem has a solution.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Fabio Difonzo, Pawel Przybylowicz, Yue Wu
Summary: This paper focuses on the existence, uniqueness, and approximation of solutions of delay differential equations (DDEs) with Caratheodory type right-hand side functions. It presents the construction of the randomized Euler scheme for DDEs and investigates its error. Furthermore, the paper reports the results of numerical experiments.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Priyanka Roy, Geetanjali Panda, Dong Qiu
Summary: In this article, a gradient based descent line search scheme is proposed for solving interval optimization problems under generalized Hukuhara differentiability. The innovation and importance of these concepts are presented from practical and computational perspectives. The necessary condition for existence of critical point is presented in inclusion form of interval-valued gradient. Suitable efficient descent direction is chosen based on the monotonic property of the interval-valued function and specific interval ordering. Mathematical convergence of the scheme is proved under the assumption of Inexact line search. The theoretical developments are implemented with a set of interval test problems in different dimensions. A possible application in finance is provided and solved by the proposed scheme.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Zhongqian Wang, Changqing Ye, Eric T. Chung
Summary: In this paper, the constrained energy minimizing generalized multiscale finite element method (CEM-GMsFEM) with mixed boundary conditions for elasticity equations in high contrast media is developed. The method offers advantages such as independence of target region's contrast from precision and significant impact of oversampling domain sizes on numerical accuracy. Furthermore, this is the first proof of convergence of CEM-GMsFEM with mixed boundary conditions for elasticity equations. Numerical experiments demonstrate the method's performance.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Samaneh Soradi-Zeid, Maryam Alipour
Summary: The Laguerre polynomials are a new set of basic functions used to solve a specific class of optimal control problems specified by integro-differential equations, namely IOCP. The corresponding operational matrices of derivatives are calculated to extend the solution of the problem in terms of Laguerre polynomials. By considering the basis functions and using the collocation method, the IOCP is simplified into solving a system of nonlinear algebraic equations. The proposed method has been proven to have an error bound and convergence analysis for the approximate optimal value of the performance index. Finally, examples are provided to demonstrate the validity and applicability of this technique.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Almudena P. Marquez, Maria L. Gandarias, Stephen C. Anco
Summary: A generalization of the KP equation involving higher-order dispersion is studied. The Lie point symmetries and conservation laws of the equation are obtained using Noether's theorem and the introduction of a potential. Sech-type line wave solutions are found and their features, including dark solitary waves on varying backgrounds, are discussed.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Susanne Saminger-Platz, Anna Kolesarova, Adam Seliga, Radko Mesiar, Erich Peter Klement
Summary: In this article, we study real functions defined on the unit square satisfying basic properties and explore the conditions for generating bivariate copulas using parameterized transformations and other constructions.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Lulu Tian, Nattaporn Chuenjarern, Hui Guo, Yang Yang
Summary: In this paper, a new local discontinuous Galerkin (LDG) algorithm is proposed to solve the incompressible Euler equation in two dimensions on overlapping meshes. The algorithm solves the vorticity, velocity field, and potential function on different meshes. The method employs overlapping meshes to ensure continuity of velocity along the interfaces of the primitive meshes, allowing for the application of upwind fluxes. The article introduces two sufficient conditions to maintain the maximum principle of vorticity.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Cheng Wang, Jilu Wang, Steven M. Wise, Zeyu Xia, Liwei Xu
Summary: In this paper, a temporally second-order accurate numerical scheme for the Cahn-Hilliard-Magnetohydrodynamics system of equations is proposed and analyzed. The scheme utilizes a modified Crank-Nicolson-type approximation for time discretization and a mixed finite element method for spatial discretization. The modified Crank-Nicolson approximation allows for mass conservation and energy stability analysis. Error estimates are derived for the phase field, velocity, and magnetic fields, and numerical examples are presented to validate the proposed scheme's theoretical results.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Mingyu He, Wenyuan Liao
Summary: This paper presents a numerical method for solving reaction-diffusion equations in spatially heterogeneous domains, which are commonly used to model biological applications. The method utilizes a fourth-order compact alternative directional implicit scheme based on Pade approximation-based operator splitting techniques. Stability analysis shows that the method is unconditionally stable, and numerical examples demonstrate its high efficiency and high order accuracy in both space and time.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
