Nonstandard discretizations of the generalized Nagumo reaction-diffusion equation

被引：39

作者：

Chen, Z

Gumel, AB

Mickens, RE

机构：

[1] Univ Manitoba, Dept Math, Winnipeg, MB R3T 2N2, Canada

[2] Clark Atlanta Univ, Dept Phys, Atlanta, GA 30314 USA

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2003年 / 19卷 / 03期

关键词：

nonstandard finite-difference schemes; truncation errors; convergence; Nagumo model; positivity;

D O I：

10.1002/num.10048

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A competitive nonstandard semi-explicit finite-difference method is constructed and used to obtain numerical solutions of the diffusion-free generalized Nagumo equation. Qualitative stability analysis and numerical simulations show that this scheme is more robust in comparison to some standard explicit methods such as forward Euler and the fourth-order Runge-Kutta method (RK4). The nonstandard scheme is extended to construct a semi-explicit and an implicit scheme to solve the full Nagumo reaction-diffusion equation. (C) 2003 Wiley Periodicals, Inc.

引用

页码：363 / 379

页数：17

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