Error analysis of an ADI scheme for the two-dimensional fractal mobile/immobile transport equation with weakly singular solutions

被引：2

作者：

Liu, Weizhi ^{[1
]}

Chen, Hu ^{[1
]}

Zaky, Mahmoud ^{[2
,3
]}

机构：

[1] Ocean Univ China, Sch Math Sci, Qingdao 266100, Peoples R China

[2] Imam Mohammad Ibn Saud Islamic Univ IMSIU, Coll Sci, Dept Math & Stat, Riyadh, Saudi Arabia

[3] Natl Res Ctr, Dept Appl Math, Cairo 12622, Egypt

来源：

APPLIED NUMERICAL MATHEMATICS | 2025年 / 210卷

基金：

中国国家自然科学基金;

关键词：

ADI scheme; Mobile/immobile transport equation; Stability; Convergence; TIME;

D O I：

10.1016/j.apnum.2024.12.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work, we consider a numerical approximation for the two-dimensional fractal mobile/immobile transport equation with weakly singular solutions, where the time first-order derivative is discretized by the backward Euler method, and the Caputo fractional derivative is approximated by the L1 scheme on a uniform mesh. The fully discrete ADI scheme is established by adding a high-order term. The stability and the convergence analyses of the fully discrete ADI scheme are analyzed in L 2-norm and H 1-norm. The numerical results show that the error estimates are sharp.

引用

页码：113 / 122

页数：10

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