Finite Difference Schemes for Time Fractional Diffusion Equations with Periodic Boundary Conditions

Zhang Hui-qin; Wang Zhi-bo

doi:10.12052/gdutxb.180122

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Finite Difference Schemes for Time Fractional Diffusion Equations with Periodic Boundary Conditions

更新时间：2026-05-27

- Finite Difference Schemes for Time Fractional Diffusion Equations with Periodic Boundary Conditions
- Vol. 36, Issue 3, Pages: 74-79(2019)
- 作者机构：
  
  广东工业大学　应用数学学院,广东,广州,510520
- 作者简介：
- 基金信息：
- DOI：10.12052/gdutxb.180122
  CLC： 35R11;65M06;65M12;65M15
- Online First：09 May 2019，
  
  Published：2019
- 稿件说明：
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张会琴, 汪志波. 带周期边界的时间分数阶扩散方程的差分格式[J]. 广东工业大学学报, 2019, 36(3): 74-79.

Zhang Hui-qin, Wang Zhi-bo. Finite Difference Schemes for Time Fractional Diffusion Equations with Periodic Boundary Conditions[J]. 2019, 36(3): 74-79.
张会琴, 汪志波. 带周期边界的时间分数阶扩散方程的差分格式[J]. 广东工业大学学报, 2019, 36(3): 74-79. DOI： 10.12052/gdutxb.180122.

Zhang Hui-qin, Wang Zhi-bo. Finite Difference Schemes for Time Fractional Diffusion Equations with Periodic Boundary Conditions[J]. 2019, 36(3): 74-79. DOI： 10.12052/gdutxb.180122.

摘要

鉴于分数阶方程的解析解实难求得

本文主要研究了带周期边界的时间分数阶扩散方程的有限差分方法

时间方向采用

2-1

离散公式

空间方向采用二阶差分格式离散

数值格式整体可达到二阶精度. 随后利用Fourier方法证明了有限差分格式的唯一可解性、稳定性和收敛性. 最后用 MATLAB语言对具体的模型进行了数值求解

数值实验能很好地印证理论结果.

Abstract

Generally

the analytic solution for fractional differential equations is hard to obtain. The difference scheme of time fractional diffusion equations with periodic boundaries is mainly studied

adopting the

2-1

formula in temporal direction

and the second order difference approximation in spatial direction. The proposed scheme can obtain second order accuracy globally. The unique solvability

stability and convergence of the proposed scheme are proved by the Fourier method. Finally

the specific fractional models are solved numerically by MATLAB language. Numerical experiments are carried out to support the theoretical results.

关键词

Keywords

references

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