A second-order scheme for a time-fractional diffusion equation

被引：5

作者：

Cen, Zhongdi ^{[1
]}

Huang, Jian ^{[1
]}

Le, Anbo ^{[1
]}

Xu, Aimin ^{[1
]}

机构：

[1] Zhejiang Wanli Univ, Inst Math, Ningbo, Zhejiang, Peoples R China

来源：

APPLIED MATHEMATICS LETTERS | 2019年 / 90卷

关键词：

Fractional differential equation; Caputo derivative; Singularity; Graded mesh;

D O I：

10.1016/j.aml.2018.10.016

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A reaction-diffusion problem with a Caputo time derivative is considered. An integral discretization scheme on a graded mesh along with a decomposition of the exact solution is proposed. It is shown that the scheme is second-order convergent, which exhibits an enhancement in the convergence rate compared with the L1 schemes. Numerical experiments are presented to support the theoretical result. (C) 2018 Elsevier Ltd. All rights reserved.

引用

页码：79 / 85

页数：7

共 50 条

[41] ERROR ANALYSIS OF A FINITE DIFFERENCE METHOD ON GRADED MESHES FOR A TIME-FRACTIONAL DIFFUSION EQUATION
Stynes, Martin
O'Riordan, Eugene
Luis Gracia, Jose
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2017, 55 (02) : 1057 - 1079
[42] Energy stability of a temporal variable-step difference scheme for time-fractional nonlinear fourth-order reaction-diffusion equation
Sun, Hong
Cao, Wanrong
Zhang, Ming
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2023, 100 (05) : 991 - 1008
[43] A direct discontinuous Galerkin method for time-fractional diffusion equation with discontinuous diffusive coefficient
Huang, Chaobao
An, Na
Yu, Xijun
Zhang, Huili
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2020, 65 (09) : 1445 - 1461
[44] A robust higher-order numerical technique with graded and harmonic meshes for the time-fractional diffusion-advection-reaction equation
Taneja, Komal
Deswal, Komal
Kumar, Devendra
MATHEMATICS AND COMPUTERS IN SIMULATION, 2023, 213 : 348 - 373
[45] ON AN OPTIMAL CONTROL PROBLEM OF TIME-FRACTIONAL ADVECTION-DIFFUSION EQUATION
Tang, Qing
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2020, 25 (02): : 761 - 779
[46] A high-order numerical scheme based on graded mesh and its analysis for the two-dimensional time-fractional convection-diffusion equation
Roul, Pradip
Rohil, Vikas
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2022, 126 : 1 - 13
[47] Numerical scheme with convergence for a generalized time-fractional Telegraph-type equation
Kumar, Kamlesh
Pandey, Rajesh K.
Sharma, Shiva
Xu, Yufeng
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2019, 35 (03) : 1164 - 1183
[48] An efficient numerical method for a time-fractional telegraph equation
Huang, Jian
Cen, Zhongdi
Xu, Aimin
MATHEMATICAL BIOSCIENCES AND ENGINEERING, 2022, 19 (05) : 4672 - 4689
[49] Analytical and numerical solutions of time-fractional advection-diffusion-reaction equation
Maji, Sandip
Natesan, Srinivasan
APPLIED NUMERICAL MATHEMATICS, 2023, 185 : 549 - 570
[50] A numerical approach for nonlinear time-fractional diffusion equation with generalized memory kernel
Seal, Aniruddha
Natesan, Srinivasan
NUMERICAL ALGORITHMS, 2024, 97 (02) : 539 - 565

← 1 2 3 4 5 →