Mixed finite element algorithm for a nonlinear time fractional wave model

被引：9

作者：

Wang, Jinfeng ^{[1
]}

Yin, Baoli ^{[2
]}

Liu, Yang ^{[2
]}

Li, Hong ^{[2
]}

Fang, Zhichao ^{[2
]}

机构：

[1] Inner Mongolia Univ Finance & Econ, Sch Stat & Math, Hohhot 010070, Peoples R China

[2] Inner Mongolia Univ, Sch Math Sci, Hohhot 010021, Peoples R China

来源：

MATHEMATICS AND COMPUTERS IN SIMULATION | 2021年 / 188卷

基金：

中国国家自然科学基金;

关键词：

Time fractional wave model; Mixed element algorithm; Stability; Optimal error estimates; ACCURATE NUMERICAL-METHOD; DIFFERENCE SCHEME; COLLOCATION METHOD; DIFFUSION PROBLEM; SUB-DIFFUSION; EQUATION; APPROXIMATIONS; SUBDIFFUSION; CONVERGENCE;

D O I：

10.1016/j.matcom.2021.03.038

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

In this article, a mixed element algorithm is presented to look for the numerical solution for a class of nonlinear wave model with the Caputo fractional derivative. By introducing two auxiliary functions and reducing order technique of fractional derivative, the studied model with high-order derivative in time is transformed into a coupled system including three lower order equations. Next, a fully discrete mixed element algorithm is formulated, where the temporal direction is approximated by a second-order scheme. The stability analysis of the proposed mixed scheme is done and optimal error estimates for three functions are derived. Finally, the numerical tests are carried out to verify the theory results. (C) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

引用

页码：60 / 76

页数：17

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