A nonstandard finite-difference scheme for the Lotka-Volterra system

被引：83

作者：

Mickens, RE ^{[1
]}

机构：

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

来源：

APPLIED NUMERICAL MATHEMATICS | 2003年 / 45卷 / 2-3期

关键词：

D O I：

10.1016/S0168-9274(02)00223-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Most numerical integration schemes for the Lotka-Volterra system have the property that the computed solutions spiral when in fact the actual solutions are periodic corresponding to closed curves. We show that a direct application of the nonstandard methods of Mickens allows the construction of a finite-difference scheme that is dynamically consistent with the differential equations. Numerical results are given to support this result. (C) 2002 IMACS. Published by Elsevier Science B.V. All rights reserved.

引用

页码：309 / 314

页数：6

共 7 条

[1] Non-standard discretization methods for some biological models [J].

Al-Kahby, H ;

Dannan, F ;

Elaydi, S .

APPLICATIONS OF NONSTANDARD FINITE DIFFERENCE SCHEMES, 2000, :155-180

[2]

KAHAN W, 1993, UNPUB LECT NOTES

[3]

Mickens R.E., 1994, Nonstandard Finite Difference Models of Differential Equations, DOI 10.1142/2081

[4]

Mickens RE, 2000, APPL NONSTANDARD FIN

[5]

Murray J.D, 1989, Mathematical Biology, V19

[6] AN UNCONVENTIONAL SYMPLECTIC INTEGRATOR OF KAHAN,W. [J].

SANZSERNA, JM .

APPLIED NUMERICAL MATHEMATICS, 1994, 16 (1-2) :245-250

[7]

[No title captured]

← 1 →