Contributions to the mathematics of the nonstandard finite difference method and applications

被引：204

作者：

Anguelov, R

Lubuma, JMS

机构：

[1] Univ Pretoria, Dept Math & Appl Math, ZA-0002 Pretoria, South Africa

[2] Vista Univ, Dept Math & Stat, ZA-0127 Pretoria, South Africa

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2001年 / 17卷 / 05期

关键词：

nonstandard finite differences; elementary stability; schemes preserving physical properties;

D O I：

10.1002/num.1025

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We formalize the transfer of essential properties of the solution of a differential equation to the solution of a discrete scheme as qualitative stability with respect to the properties. This permits us to motivate some rules (viz. on the order of the difference equation, on the renormalization of the denominator of the discrete derivative, and on nonlocal approximation of nonlinear terms) used in the design of nonstandard finite difference schemes. Extensions of some models are considered, and numerical examples confirming the efficiency of the nonstandard approach are provided. (C) 2001 John Wiley & Sons, Inc.

引用

页码：518 / 543

页数：26

共 22 条

[1]

[Anonymous], 1971, NUMERICAL INITIAL VA

[2]

[Anonymous], HDB NUMERICAL ANAL F

[3]

Butcher J. C., 1987, The Numerical Analysis of Ordinary Differential Equations: Runge-Kutta and General Linear Methods

[4]

Forsythe G.E., 1960, FINITE DIFFERENCE ME

[5]

Gautschi W., 1961, NUMER MATH, V3, P381, DOI DOI 10.1007/BF01386037

[6]

KELLER HB, 1975, MATH COMPUT, V29, P464, DOI 10.1090/S0025-5718-1975-0371058-7

[7]

Kojouharov HV, 1999, NUMER METH PART D E, V15, P617, DOI 10.1002/(SICI)1098-2426(199911)15:6<617::AID-NUM1>3.3.CO

[8]

2-D

[9]

LAMBERT JD, 1991, NUMERICAL METHODS OR

[10]

Mickens R, 1999, THEOR COMPUT ACOUST, V97, P419

← 1 2 3 →