A second-order box solver for nonlinear delayed convection-diffusion equations with Neumann boundary conditions

被引：4

作者：

Deng, Dingwen ^{[1
,2
]}

Xie, Jianqiang ^{[1
]}

Jiang, Yaolin ^{[2
]}

Liang, Dong ^{[3
]}

机构：

[1] Nanchang Hangkong Univ, Coll Math & Informat Sci, Nanchang 330063, Jiangxi, Peoples R China

[2] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Shaanxi, Peoples R China

[3] York Univ, Dept Math & Stat, Toronto, ON, Canada

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2019年 / 96卷 / 09期

基金：

加拿大自然科学与工程研究理事会; 中国国家自然科学基金;

关键词：

Nonlinear convection-diffusion equations with delays; Neumann boundary conditions; box scheme; convergence; solvability; COMPACT DIFFERENCE SCHEME; ASYMPTOTIC STABILITY; PARABOLIC EQUATIONS; CONVERGENCE; SYSTEMS;

D O I：

10.1080/00207160.2018.1542133

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, by applying order reduction approach, a second-order accurate box scheme is established to solve a nonlinear delayed convection-diffusion equations with Neumann boundary conditions. By the discrete energy method, it is shown that the difference scheme is uniquely solvable, and has a convergence rate of with respect to - norm in constrained and non-constrained temporal grids. Besides, for constrained temporal step, a Richardson extrapolation method (REM) used along with the box scheme, which makes final solution third-order accurate in both time and space, is developed in detail. Finally, numerical results confirm the accuracy and efficiency of our solvers.

引用

页码：1879 / 1898

页数：20

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