Non standard finite difference scheme preserving dynamical properties

被引：40

作者：

Cresson, Jacky ^{[1
,2
]}

Pierret, Frederic ^{[2
,3
]}

机构：

[1] Univ Pau & Pays Adour, Lab Math Appl Pau, Ave Univ,BP 1155, F-64013 Pau, France

[2] Univ Paris 06, Sorbonne Univ, Observ Paris, SYRTE,PSL Res Univ,CNRS,LNE, F-75252 Paris 05, France

[3] Univ Lille, Univ Paris 06, Sorbonne Univ, IMCCE,Observ Paris,PSL Res Univ,CNRS, Lille, France

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2016年 / 303卷

关键词：

Non-standard finite difference methods; Qualitative behaviour; Qualitative dynamics preserving numerical scheme; PREDATOR-PREY MODELS; NUMERICAL-METHODS; NONSTANDARD; CONSISTENCY; SYSTEMS;

D O I：

10.1016/j.cam.2016.02.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the construction of a non-standard finite differences numerical scheme for a general class of two dimensional differential equations including several models in population dynamics using the idea of non-local approximation introduced by R. Mickens. We prove the convergence of the scheme, the unconditional, with respect to the discretization parameter, preservation of the fixed points of the continuous system and the preservation of their stability nature. Several numerical examples are given and comparison with usual numerical scheme (Euler, Runge-Kutta of order 2 or 4) is detailed. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：15 / 30

页数：16

共 24 条

[1] Contributions to the mathematics of the nonstandard finite difference method and applications [J].