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

Yang Xu; Yanming Zhang; Jingjun Zhao

doi:10.1016/j.amc.2019.124664

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

Yang Xu
, Yanming Zhang
, Jingjun Zhao^*

^*Corresponding author for this work

School of Mathematics

Harbin Institute of Technology

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

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.

Original language	English
Article number	124664
Journal	Applied Mathematics and Computation
Volume	364
DOIs	https://doi.org/10.1016/j.amc.2019.124664
State	Published - 1 Jan 2020

Keywords

Convergence
General linear method
Riesz space fractional diffusion equation
Spectral Galerkin method
Stability

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10.1016/j.amc.2019.124664

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title = "General linear and spectral Galerkin methods for the Riesz space fractional diffusion equation",

abstract = "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.",

keywords = "Convergence, General linear method, Riesz space fractional diffusion equation, Spectral Galerkin method, Stability",

author = "Yang Xu and Yanming Zhang and Jingjun Zhao",

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year = "2020",

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T1 - General linear and spectral Galerkin methods for the Riesz space fractional diffusion equation

AU - Xu, Yang

AU - Zhang, Yanming

AU - Zhao, Jingjun

PY - 2020/1/1

Y1 - 2020/1/1

N2 - 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.

AB - 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.

KW - Convergence

KW - General linear method

KW - Riesz space fractional diffusion equation

KW - Spectral Galerkin method

KW - Stability

UR - https://www.scopus.com/pages/publications/85070609165

U2 - 10.1016/j.amc.2019.124664

DO - 10.1016/j.amc.2019.124664

M3 - 文章

AN - SCOPUS:85070609165

SN - 0096-3003

VL - 364

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

M1 - 124664

ER -

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

Abstract

Keywords

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