A second-order scheme with nonuniform time grids for Caputo-Hadamard fractional sub-diffusion equations?

被引：40

作者：

Wang, Zhibo ^{[1
]}

Ou, Caixia ^{[1
]}

Vong, Seakweng ^{[2
]}

机构：

[1] Guangdong Univ Technol, Sch Math & Stat, Guangzhou 510006, Guangdong, Peoples R China

[2] Univ Macau, Dept Math, Taipa, Macao, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2022年 / 414卷

基金：

中国国家自然科学基金;

关键词：

Caputo-Hadamard derivative; Nonuniform meshes; Weak singularity; Error convolution structure; Global consistency analysis; SHARP ERROR ESTIMATE; NUMERICAL-METHOD; GRADED MESHES; FORMULA; STEPS;

D O I：

10.1016/j.cam.2022.114448

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a second-order scheme with nonuniform time meshes for Caputo- Hadamard fractional sub-diffusion equations with initial singularity is investigated. Firstly, a Taylor-like formula with integral remainder is proposed, which is crucial to studying the discrete convolution kernels and error estimate. Secondly, we come up with an error convolution structure (ECS) analysis for Llog,2-1 sigma interpolation approximation to the Caputo-Hadamard fractional derivative. The core result in this paper is an ECS bound and a global consistency analysis established at an offset point. By virtue of this result, we obtain a sharp L2-norm error estimate of a second-order Crank-Nicolson-like scheme for Caputo-Hadamard fractional differential equations. Ultimately, an example is presented to show the sharpness of our analysis. (c) 2022 Elsevier B.V. All rights reserved.

引用

页数：18

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