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
收藏
页码：1879 / 1898
页数：20
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