时间分数阶对流-扩散方程的有限差分解法

马燕, MUSBAH F.S.

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

数学季刊 >

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

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

时间分数阶对流-扩散方程的有限差分解法

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

收稿日期: 2018-09-04

网络出版日期: 2020-08-23

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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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马燕, MUSBAH F.S. . 时间分数阶对流-扩散方程的有限差分解法[J]. 数学季刊, 2019 , 34(3) : 259 -273 . DOI: 10.13371/j.cnki.chin.q.j.m.2019.03.004

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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