A fast L1 formula on tanh meshes for time fractional Burgers equations

被引：0

作者：

Xing, Zhiyong ^{[1
,2
]}

Sun, Wenbing ^{[1
]}

Zhu, Xiaogang ^{[1
]}

机构：

[1] Shaoyang Univ, Dept Math, Shaoyang 422000, Hunan, Peoples R China

[2] Key Lab Math Modellingand High Performance Comp Ai, Nanjing 211106, Peoples R China

来源：

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS | 2024年

关键词：

Time fractional Burgers equation; Caputo fractional derivative; weak singularity; the tanh meshes; nonuniformL1; method; CONSERVATIVE DIFFERENCE SCHEME; IMPLEMENTATION;

D O I：

10.1142/S0219887824400413

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper, a fast L1 formula on tanh meshes is proposed for time fractional Burgers equations with Caputo fractional derivative. The solvability, boundness and convergence of the numerical scheme are rigorously established. Several numerical experiments are provided to support the theoretical results. The results of the experiments showed that the proposed numerical method cannot only effectively deal with the weak singularity of the problem near t = 0, but also significantly reduce the computational complexity of numerical simulation.

引用

页数：15

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