带非线性源项的Riesz回火分数阶扩散方程的预估校正方法

doi:10.12286/jssx.j2021-0803

计算数学 ›› 2023, Vol. 45 ›› Issue (1): 22-38.DOI: 10.12286/jssx.j2021-0803

带非线性源项的Riesz回火分数阶扩散方程的预估校正方法

肖滴琴, 曹学年

湘潭大学数学与计算科学学院, 湘潭 411105

收稿日期:2021-04-14 出版日期:2023-02-14 发布日期:2023-02-13
通讯作者: 曹学年,Email: cxn@xtu.edu.cn
基金资助:
国家自然科学基金(12071403)资助.

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肖滴琴, 曹学年. 带非线性源项的Riesz回火分数阶扩散方程的预估校正方法[J]. 计算数学, 2023, 45(1): 22-38.

Xiao Diqin, Cao Xuenian. PREDICTOR-CORRECTOR APPROACH FOR RIESZ TEMPERED FRACTIONAL DIFFUSION EQUATION WITH A NONLINEAR SOURCE TERM[J]. Mathematica Numerica Sinica, 2023, 45(1): 22-38.

PREDICTOR-CORRECTOR APPROACH FOR RIESZ TEMPERED FRACTIONAL DIFFUSION EQUATION WITH A NONLINEAR SOURCE TERM

Xiao Diqin, Cao Xuenian

School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China

Received:2021-04-14 Online:2023-02-14 Published:2023-02-13
Supported by:
The project was supported by the National Key Research and Development Program of China (2019YFC1905301);National Natural Science Foundation of China (22078115,21776108,21690083,22008078).

本文针对带非线性源项的 Riesz 回火分数阶扩散方程, 利用预估校正方法离散时间偏导数, 并用修正的二阶 Lubich 回火差分算子逼近 Riesz 空间回火的分数阶偏导数, 构造出一类新的数值格式. 给出了数值格式在一定条件下的稳定性与收敛性分析, 且该格式的时间与空间收敛阶均为二阶. 数值试验表明数值方法是有效的.

关键词： Riesz回火分数阶扩散方程, 预估校正法, 修正的二阶Lubich回火差分算子, 稳定性, 收敛性

In this paper, a new numerical scheme is constructed for solving Riesz tempered fractional diffusion equation with a nonlinear source term in which the predictor-corrector approach is applied to discretize the time partial derivative and the modified second-order Lubich tempered difference operator is used to approximate the Riesz space tempered fractional partial derivative. The stability and convergence analysis of the numerical scheme are given under a certain condition, and there are both second order for the time and space convergence order of this numerical scheme. Numerical experiments demonstrate that the numerical method is effective.

Key words: Riesz tempered fractional diffusion equation, Predictor-Corrector approach, The modified second-order Lubich tempered difference operator, Stability, Convergence

MR(2010)主题分类:

65D17

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摘要

带非线性源项的Riesz回火分数阶扩散方程的预估校正方法

PREDICTOR-CORRECTOR APPROACH FOR RIESZ TEMPERED FRACTIONAL DIFFUSION EQUATION WITH A NONLINEAR SOURCE TERM

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