General linear and spectral Galerkin methods for the Riesz space fractional diffusion equation

被引：4

作者：

Xu, Yang ^{[1
]}

Zhang, Yanming ^{[1
]}

Zhao, Jingjun ^{[1
]}

机构：

[1] Harbin Inst Technol, Dept Math, Harbin 150001, Heilongjiang, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2020年 / 364卷 / 364期

基金：

中国国家自然科学基金;

关键词：

Riesz space fractional diffusion equation; General linear method; Spectral Galerkin method; Convergence; Stability; B-CONVERGENCE; SCHEME;

D O I：

10.1016/j.amc.2019.124664

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The general linear method is considered to discretize the temporal term of Riesz space fractional diffusion equation. Combined with a spectral Galerkin method in the spatial direction, a method with high global accuracy is constructed. If the general linear method is algebraically stable, the stability is proven for the full discretization. Furthermore, under some conditions, the convergence order in time and the optimal error estimate in space are also obtained. Meanwhile, numerical examples are given to confirm the theoretical results. (C) 2019 Elsevier Inc. All rights reserved.

引用

页数：12

共 31 条

[1] The fractional-order governing equation of Levy motion
Benson, DA
Wheatcraft, SW
Meerschaert, MM
[J]. WATER RESOURCES RESEARCH, 2000, 36 (06) : 1413 - 1423
[2] An h-p version of the continuous Petrov-Galerkin finite element method for Riemann-Liouville fractional differential equation with novel test basis functions
Bu, Weiping
Xiao, Aiguo
[J]. NUMERICAL ALGORITHMS, 2019, 81 (02) : 529 - 545
[3] Galerkin finite element method for two-dimensional Riesz space fractional diffusion equations
Bu, Weiping
Tang, Yifa
Yang, Jiye
[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2014, 276 : 26 - 38
[4] Burrage K., 1980, BIT (Nordisk Tidskrift for Informationsbehandling), V20, P185, DOI 10.1007/BF01933191
[5] FOURTH ORDER ACCURATE SCHEME FOR THE SPACE FRACTIONAL DIFFUSION EQUATIONS
Chen, Minghua
Deng, Weihua
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2014, 52 (03) : 1418 - 1438
[6] GENERALIZED JACOBI FUNCTIONS AND THEIR APPLICATIONS TO FRACTIONAL DIFFERENTIAL EQUATIONS
Chen, Sheng
Shen, Jie
Wang, Li-Lian
[J]. MATHEMATICS OF COMPUTATION, 2016, 85 (300) : 1603 - 1638
[7] HIGH-ORDER ALGORITHMS FOR RIESZ DERIVATIVE AND THEIR APPLICATIONS (III)
Ding, Hengfei
Li, Changpin
[J]. FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2016, 19 (01) : 19 - 55
[8] Variational solution of fractional advection dispersion equations on bounded domains in Rd
Ervin, Vincent J.
Roop, John Paul
[J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2007, 23 (02) : 256 - 281
[9] Variational formulation for the stationary fractional advection dispersion equation
Ervin, VJ
Roop, JP
[J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2006, 22 (03) : 558 - 576
[10] Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces
Guo, BY
Wang, LL
[J]. JOURNAL OF APPROXIMATION THEORY, 2004, 128 (01) : 1 - 41

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