An Efficient Compact Difference Method for the Fourth-order Nonlocal Subdiffusion Problem

被引：5

作者：

Yang, Xuehua ^{[1
]}

Wang, Wan ^{[1
]}

Zhou, Ziyi ^{[1
]}

Zhang, Haixiang ^{[1
]}

机构：

[1] Hunan Univ Technol, Sch Sci, Zhuzhou 412007, Peoples R China

来源：

TAIWANESE JOURNAL OF MATHEMATICS | 2025年 / 29卷 / 01期

基金：

中国国家自然科学基金;

关键词：

fourth order subdiffusion equation; compact finite difference method; stability and convergence; PARTIAL INTEGRODIFFERENTIAL EQUATION; DISCONTINUOUS GALERKIN METHOD; FINITE-ELEMENT-METHOD; EVOLUTION EQUATION; NUMERICAL-METHOD; GRADED MESHES; SCHEME;

D O I：

10.11650/tjm/240906

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, a compact finite difference scheme is constructed and studied for the fourth-order subdiffusion equation with the Riemann-Liouville fractional integral. The Caputo time-fractional derivative term and the Riemann-Liouville fractional integral term are discretized by L1-2 discrete formula and second order convolution quadrature rule, respectively. By using the discrete energy method, the Cholesky decomposition method and the reduced-order method, the stability and convergence are attained. And the convergence orders are reached second-order in time and fourthorder in space. Numerical examples verify the theoretical analysis.

引用

页码：35 / 66

页数：32

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