A Linearized Second-Order Difference Scheme for the Nonlinear Time-Fractional Fourth-Order Reaction-Diffusion Equation

被引：7

作者：

Sun, Hong ^{[1
]}

Sun, Zhi-zhong ^{[2
]}

Du, Rui ^{[2
]}

机构：

[1] Nanjing Inst Technol, Dept Math & Phys, Nanjing 211167, Jiangsu, Peoples R China

[2] Southeast Univ, Sch Math, Nanjing 210096, Jiangsu, Peoples R China

来源：

NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS | 2019年 / 12卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Fractional differential equation; Caputo derivative; high order equation; nonlinear; linearized; difference scheme; convergence; stability; FINITE-ELEMENT-METHOD; APPROXIMATIONS; ALGORITHMS;

D O I：

10.4208/nmtma.OA-2017-0144

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper presents a second-order linearized finite difference scheme for the nonlinear time-fractional fourth-order reaction-diffusion equation. The temporal Caputo derivative is approximated by L2-1(sigma) formula with the approximation order of O(tau(3-alpha)). The unconditional stability and convergence of the proposed scheme are proved by the discrete energy method. The scheme can achieve the global second-order numerical accuracy both in space and time. Three numerical examples are given to verify the numerical accuracy and efficiency of the difference scheme.

引用

页码：1168 / 1190

页数：23

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