一种新的四阶分组迭代法求解具有弱初始奇异性的时间分数次扩散方程

IF 1.8 3区数学 Q1 MATHEMATICS

AIMS Mathematics Pub Date : 2023-01-01 DOI:10.3934/math.2023697

Muhammad Asim Khan, N. Alias, Umair Ali

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引用次数: 3

摘要

构造了分数阶次扩散方程数值解的一种新的四阶显式分组迭代方法。采用四阶有限差分法对方程进行离散化。在时间上使用具有弱奇点函数的捕获分数离散化，同样地，利用四阶近似来逼近空间导数。进一步分析了该方案的收敛性和稳定性。最后通过数值算例验证了该方法的准确性和有效性。

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A new fourth-order grouping iterative method for the time fractional sub-diffusion equation having a weak singularity at initial time

A new fourth-order explicit grouping iterative method is constructed for the numerical solution of the fractional sub-diffusion equation. The discretization of the equation is based on fourth-order finite difference method. Captive fractional discretization having functions with a weak singularity at $ t = 0 $ is used for time and similarly, the space derivative is approximated with the help of fourth-order approximation. Furthermore, the convergence and stability of the scheme are analyzed. Finally, the accuracy and validity are investigated by some numerical examples.

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来源期刊

AIMS Mathematics Mathematics-General Mathematics

CiteScore

3.40

自引率

13.60%

发文量

769

审稿时长

90 days

期刊介绍： AIMS Mathematics is an international Open Access journal devoted to publishing peer-reviewed, high quality, original papers in all fields of mathematics. We publish the following article types: original research articles, reviews, editorials, letters, and conference reports.