时间延迟扩散-波动分数阶微分方程有限差分方法

doi:10.12286/jssx.2019.1.82

计算数学 ›› 2019, Vol. 41 ›› Issue (1): 82-90.DOI: 10.12286/jssx.2019.1.82

时间延迟扩散-波动分数阶微分方程有限差分方法

王志强¹, 文立平¹, 朱珍民²

1. 湘潭大学数学与计算科学学院, 湘潭 411105;
2. 中国科学院计算技术研究所, 北京 100190

收稿日期:2017-10-26 出版日期:2019-03-15 发布日期:2019-02-18

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王志强, 文立平, 朱珍民. 时间延迟扩散-波动分数阶微分方程有限差分方法[J]. 计算数学, 2019, 41(1): 82-90.

Wang Zhiqiang, Wen Liping, Zhu Zhenmin. FINITE DIFFERENCE METHOD FOR TIME DELAY DIFFUSION-WAVE FRACTIONAL DIFFERENTIAL EQUATIONS[J]. Mathematica Numerica Sinica, 2019, 41(1): 82-90.

FINITE DIFFERENCE METHOD FOR TIME DELAY DIFFUSION-WAVE FRACTIONAL DIFFERENTIAL EQUATIONS

Wang Zhiqiang¹, Wen Liping¹, Zhu Zhenmin²

1. School of Mathematics and Computing Science, Xiangtan University, Xiangtan 411105, China;
2. Institute of Computing and Technology, Chinese Academy of Sciences, Beijing 100190, China

Received:2017-10-26 Online:2019-03-15 Published:2019-02-18

本文提出求解时间延迟扩散-波动分数阶微分方程有限差分方法，方程中对时间的一阶导函数用α阶（0 < α < 1） Caputo分数阶导数代替.文章中利用Lubich线性多步法对分数阶微分进行差分离散，且文章利用分段区间证明该方法是稳定的，且利用数值实验加以验证.

关键词： 时间延迟扩散-波动分数阶微分方程, 有限差分, 稳定性分析, 收敛性分析

This paper presents a finite difference method for solving time delay diffusion-wave fractional differential equations, we instead the first order of time by α order (0 < α < 1) Caputo fractional differential derivative in equations. In this paper, the fractional differential is discretized by the Lubich linear multistep method, and the paper uses the segmented interval to prove the stability of the algorithm, and it is validated by numerical experiments.

Key words: time delay diffusion-wave fractional differential eqations, finit different method, stability analysis

MR(2010)主题分类:

65D17

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摘要

时间延迟扩散-波动分数阶微分方程有限差分方法

FINITE DIFFERENCE METHOD FOR TIME DELAY DIFFUSION-WAVE FRACTIONAL DIFFERENTIAL EQUATIONS

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