带漂移的单侧正规化回火分数阶扩散方程的Crank-Nicolson拟紧格式

doi:10.12286/jssx.j2019-0608

计算数学 ›› 2021, Vol. 43 ›› Issue (2): 210-226.DOI: 10.12286/jssx.j2019-0608

带漂移的单侧正规化回火分数阶扩散方程的Crank-Nicolson拟紧格式

邱泽山, 曹学年

湘潭大学数学与计算科学学院, 湘潭 411105

收稿日期:2019-07-25 出版日期:2021-04-15 发布日期:2021-05-13
通讯作者: 曹学年,cxn@xtu.edu.cn.
基金资助:
国家自然科学基金（12071403）资助.

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邱泽山, 曹学年. 带漂移的单侧正规化回火分数阶扩散方程的Crank-Nicolson拟紧格式[J]. 计算数学, 2021, 43(2): 210-226.

Qiu Zeshan, Cao Xuenian. CRANK-NICOLSON QUASI-COMPACT SCHEMES FOR ONE-SIDED NORMALIZED TEMPERED FRACTIONAL DIFFUSION EQUATIONS WITH DRIFT[J]. Mathematica Numerica Sinica, 2021, 43(2): 210-226.

CRANK-NICOLSON QUASI-COMPACT SCHEMES FOR ONE-SIDED NORMALIZED TEMPERED FRACTIONAL DIFFUSION EQUATIONS WITH DRIFT

Qiu Zeshan, Cao Xuenian

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

Received:2019-07-25 Online:2021-04-15 Published:2021-05-13

基于已有的针对单侧正规化回火分数阶扩散方程的三阶拟紧算法，将该算法的思想应用于带漂移的单侧正规化回火分数阶扩散方程的数值模拟，并结合Crank-Nicolson方法导出数值格式.证明了数值格式的稳定性与收敛性，且数值格式的时间收敛阶和空间收敛阶分别是二阶和三阶.通过数值试验验证了数值格式的有效性和理论结果.

关键词： 正规化回火分数阶扩散方程, 漂移, Crank-Nicolson, 稳定性, 收敛性

Based on the existed third-order quasi-compact algorithm for one-sided normalized tempered fractional diffusion equations, the idea of the algorithm is applied to the numerical simulation of the one-sided normalized tempered fractional diffusion equations with drift, and combined the Crank-Nicolson method to derive the numerical schemes. The stability and convergence of the numerical schemes are proved, and the time and space convergence orders of the numerical schemes are second and third order, respectively. The effectiveness of the numerical schemes and the theoretical results are verified by numerical experiments.

Key words: Normalized tempered fractional diffusion equations, Drift, Crank-Nicolson, Stability, Convergence

MR(2010)主题分类:

65D17

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带漂移的单侧正规化回火分数阶扩散方程的Crank-Nicolson拟紧格式

CRANK-NICOLSON QUASI-COMPACT SCHEMES FOR ONE-SIDED NORMALIZED TEMPERED FRACTIONAL DIFFUSION EQUATIONS WITH DRIFT

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