Finite Difference Methods for the Time Fractional Advection-diffusion Equation

MA Yan, MUSBAH F.S.

doi:10.13371/j.cnki.chin.q.j.m.2019.03.004

Chinese Quarterly Journal of Mathematics >

2019 , Vol. 34 >Issue 3: 259 - 273

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2019.03.004

Finite Difference Methods for the Time Fractional Advection-diffusion Equation

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Zhi Xing College of Northwest Normal University Department of Mathematics, University of Bani Walid

Received date: 2018-09-04

Online published: 2020-08-23

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Abstract

In this paper, three implicit finite difference methods are developed to solve one dimensional time fractional advection-diffusion equation. The fractional derivative is treated by applying right shifted Gr¨unwald-Letnikov formula of order α∈(0, 1). We investigate the stability analysis by using von Neumann method with mathematical induction and prove that these three proposed methods are unconditionally stable. Numerical results are presented to demonstrate the effectiveness of the schemes mentioned in this paper.

Key words： Time fractional advection-di?usion; Finite di?erence method; Gr?unwald-Letnikov formula; Stability; E?ectiveness

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MA Yan, MUSBAH F.S. . Finite Difference Methods for the Time Fractional Advection-diffusion Equation[J]. Chinese Quarterly Journal of Mathematics, 2019 , 34(3) : 259 -273 . DOI: 10.13371/j.cnki.chin.q.j.m.2019.03.004

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