Convergence and stability of compact finite difference method for nonlinear time fractional reaction-diffusion equations with delay

被引：41

作者：

Li, Lili ^{[1
,2
]}

Zhou, Boya ^{[1
,2
]}

Chen, Xiaoli ^{[1
,2
]}

Wang, Zhiyong ^{[3
]}

机构：

[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Hubei, Peoples R China

[2] Huazhong Univ Sci & Technol, Hubei Key Lab Engn Modeling & Sci Comp, Wuhan 430074, Hubei, Peoples R China

[3] Univ Elect Sci & Technol China, Sch Math Sci, Chengdu 611731, Sichuan, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2018年 / 337卷

基金：

中国国家自然科学基金;

关键词：

Nonlinear time fractional reaction-diffusion equations with delay; Fractional Gronwall type inequality; Stability; Convergence; Linearized numerical scheme; SCHRODINGER-EQUATIONS; SUBDIFFUSION EQUATION; GRONWALL INEQUALITY; PARABOLIC EQUATIONS; ELEMENT-METHOD; ERROR ANALYSIS; SCHEME; SYSTEMS; FEMS;

D O I：

10.1016/j.amc.2018.04.057

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with numerical solutions of nonlinear time fractional reaction-diffusion equations with time delay. A linearized compact finite difference scheme is proposed to solve the equations. In terms of a new developed fractional Gronwall type inequality, convergence and stability of the proposed scheme are obtained. Numerical experiments are given to illustrate the theoretical results. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：144 / 152

页数：9

共 35 条

[1] A high order schema for the numerical solution of the fractional ordinary differential equations [J].

Cao, Junying ;

Xu, Chuanju .

JOURNAL OF COMPUTATIONAL PHYSICS, 2013, 238 :154-168

[2]

Cao X., 2017, J COMPUT APPL MATH, V318, P886

[3] Finite difference methods and a fourier analysis for the fractional reaction-subdiffusion equation [J].

Chen, Chang-ming ;

Liu, F. ;

Burrage, K. .

APPLIED MATHEMATICS AND COMPUTATION, 2008, 198 (02) :754-769

[4] A compact finite difference scheme for the fractional sub-diffusion equations [J].

Gao, Guang-hua ;

Sun, Zhi-zhong .

JOURNAL OF COMPUTATIONAL PHYSICS, 2011, 230 (03) :586-595

[5] A finite difference scheme for semilinear space-fractional diffusion equations with time delay [J].

Hao, Zhaopeng ;

Fan, Kai ;

Cao, Wanrong ;

Sun, Zhizhong .

APPLIED MATHEMATICS AND COMPUTATION, 2016, 275 :238-254

[6] A stable numerical method for multidimensional time fractional Schrodinger equations [J].

Hicdurmaz, Betul ;

Ashyralyev, Allaberen .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2016, 72 (06) :1703-1713

[7] Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations [J].

Jiang, Shidong ;

Zhang, Jiwei ;

Zhang, Qian ;

Zhang, Zhimin .

COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2017, 21 (03) :650-678

[8] NUMERICAL ANALYSIS OF NONLINEAR SUBDIFFUSION EQUATIONS [J].

Jin, Bangti ;

Li, Buyang ;

Zhou, Zhi .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2018, 56 (01) :1-23

[9] TWO FULLY DISCRETE SCHEMES FOR FRACTIONAL DIFFUSION AND DIFFUSION-WAVE EQUATIONS WITH NONSMOOTH DATA [J].

Jin, Bangti ;

Lazarov, Raytcho ;

Zhou, Zhi .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2016, 38 (01) :A146-A170

[10] ERROR ESTIMATES FOR A SEMIDISCRETE FINITE ELEMENT METHOD FOR FRACTIONAL ORDER PARABOLIC EQUATIONS [J].

Jin, Bangti ;

Lazarov, Raytcho ;

Zhou, Zhi .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2013, 51 (01) :445-466

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