A Second-Order Accurate Numerical Approximation for a Two-Sided Space-Fractional Diffusion Equation-Reference-Cited by-同舟云学术

A Second-Order Accurate Numerical Approximation for a Two-Sided Space-Fractional Diffusion Equation

Published:2023-04-12 Issue:8 Volume:11 Page:1838
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Liu Taohua¹^ORCID,Yin Xiucao¹,Chen Yinghao²³^ORCID,Hou Muzhou²^ORCID

Affiliation:

1. School of Science, Shaoyang University, Shaoyang 422000, China

2. School of Mathematics and Statistics, Central South University, Changsha 410083, China

3. Eastern Institute for Advanced Study, Yongriver Institute of Technology, Ningbo 315201, China

Abstract

In this paper, we investigate a practical numerical method for solving a one-dimensional two-sided space-fractional diffusion equation with variable coefficients in a finite domain, which is based on the classical Crank-Nicolson (CN) method combined with Richardson extrapolation. Second-order exact numerical estimates in time and space are obtained. The unconditional stability and convergence of the method are tested. Two numerical examples are also presented and compared with the exact solution.

Funder

Hunan Provincial Natural Science Foundation of China

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/11/8/1838/pdf

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