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.
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页数：20
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