Finite difference method for solving fractional differential equations at irregular meshes

被引：50

作者：

Vargas, Antonio M. ^{[1
]}

机构：

[1] Univ Complutense Madrid, Dept Analisis Matemat & Matemat Aplicada, Madrid 28040, Spain

来源：

MATHEMATICS AND COMPUTERS IN SIMULATION | 2022年 / 193卷

关键词：

Meshless method; Fractional differential equations; Caputo fractional derivative; BEHAVIOR;

D O I：

10.1016/j.matcom.2021.10.010

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

This paper presents a novel meshless technique for solving a class of fractional differential equations based on moving least squares and on the existence of a fractional Taylor series for Caputo derivatives. A "Generalized Finite Difference" approach is followed in order to derive a simple discretization of the space fractional derivatives. Consistency, stability and convergence of the method are proved. Several examples illustrating the accuracy of the method are given. (C) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

引用

页码：204 / 216

页数：13

共 18 条

[1] Fractional Bernstein Series Solution of Fractional Diffusion Equations with Error Estimate [J].

Alshbool, Mohammed Hamed ;

Isik, Osman ;

Hashim, Ishak .

AXIOMS, 2021, 10 (01) :1-19

[2]

[Anonymous], 1986, Curve and Surface Fitting: An Introduction

[3] Fractional reproduction-dispersal equations and heavy tail dispersal kernels [J].

Baeumer, Boris ;

Kovacs, Mihaly ;

Meerschaert, Mark M. .

BULLETIN OF MATHEMATICAL BIOLOGY, 2007, 69 (07) :2281-2297

[4] Solving a fully parabolic chemotaxis system with periodic asymptotic behavior using Generalized Finite Difference Method [J].

Benito, J. J. ;

Garcia, A. ;

Gavete, L. ;

Negreanu, M. ;

Urena, F. ;

Vargas, A. M. .

APPLIED NUMERICAL MATHEMATICS, 2020, 157 :356-371

[5] Influence of several factors in the generalized finite difference method [J].

Benito, JJ ;

Ureña, F ;

Gavete, L .

APPLIED MATHEMATICAL MODELLING, 2001, 25 (12) :1039-1053

[6] LINEAR MODELS OF DISSIPATION WHOSE Q IS ALMOST FREQUENCY INDEPENDENT-2 [J].

CAPUTO, M .

GEOPHYSICAL JOURNAL OF THE ROYAL ASTRONOMICAL SOCIETY, 1967, 13 (05) :529-&

[7] On Multivariate Fractional Taylor's and Cauchy' Mean Value Theorem [J].

Cheng, Jinfa .

JOURNAL OF MATHEMATICAL STUDY, 2019, 52 (01) :38-52

[8] Solving second order non-linear elliptic partial differential equations using generalized finite difference method [J].

Gavete, L. ;

Urena, F. ;

Benito, J. J. ;

Garcia, A. ;

Urena, M. ;

Salete, E. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2017, 318 :378-387

[9] On the numerical solutions for the fractional diffusion equation [J].

Khader, M. M. .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2011, 16 (06) :2535-2542

[10]

Kilbas Anatoly A., 2006, Theory and Applications of Fractional Differential Equations, V204, P1

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