Analysis of BDF2 finite difference method for fourth-order integro-differential equation

被引：1

作者：

Liu, Yanling ^{[1
]}

Yang, Xuehua ^{[1
]}

Zhang, Haixiang ^{[1
]}

Liu, Yuan ^{[1
]}

机构：

[1] Hunan Univ Technol, Coll Sci, Zhuzhou 412008, Peoples R China

来源：

COMPUTATIONAL & APPLIED MATHEMATICS | 2021年 / 40卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Fractional differential equation; BDF2; scheme; Finite difference method; Stability and convergence; 65M60; 26A33; DISCONTINUOUS GALERKIN METHOD; FRACTIONAL DIFFUSION EQUATION; ELEMENT-METHOD; SCHEME;

D O I：

10.1007/s40314-021-01449-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work, the stability and error analysis are presented for fully discrete solutions of the fourth-order differential equation with the multi-term Riemann-Liouville fractional integral. Our numerical scheme is obtained by the standard central difference method in space and the formally two-step backward differentiation formula method and second-order convolution quadrature in time. Optimal order of the numerical scheme in L2-norm is established using the discrete energy method. The analysis is supported by two numerical experiments.

引用

页数：20

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