A nonstandard finite difference scheme for the diffusionless Burgers equation with logistic reaction

被引：20
|
作者：
Mickens, RE [1 ]
机构：
[1] Clark Atlanta Univ, Dept Phys, Atlanta, GA 30314 USA
来源：
MATHEMATICS AND COMPUTERS IN SIMULATION | 2003年 / 62卷 / 1-2期
关键词：
Burgers equation; nonstandard finite difference schemes; numerical integration;
D O I：
10.1016/S0378-4754(02)00180-5
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
A nonstandard finite difference scheme is constructed for the Burgers partial differential equation having no diffusion and a nonlinear logistic reaction term. This scheme preserves the positivity and boundedness properties of the original differential equation and includes the a priori requirement of being semi-explicit. Several other nonstandard discretizations are constructed and their mathematical structures discussed. All of these schemes can be used to calculate numerical solutions for traveling waves problems involving phenomena modeled by the original differential equation. (C) 2002 IMACS. Published by Elsevier Science B.V. All rights reserved.
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页码：117 / 124
页数：8
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