Discretizations of nonlinear differential equations using explicit nonstandard methods

In a recent paper, Chen and Solis investigated the appearance of spurious solutions when first-order ODEs are discretized using Runge–Kutta schemes. They concluded that the reliability of the numerical solutions to a particular ODE could be verified only by constructing several discrete models and c...

Full description

Saved in:
Bibliographic Details
Published in:Journal of computational and applied mathematics 1999-10, Vol.110 (1), p.181-185
Main Author: Mickens, Ronald E
Format: Article
Language:English
Subjects:
Exact sciences and technology
Mathematical analysis
Mathematics
Nonstandard finite difference scheme
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Sciences and techniques of general use
Spurious solution
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In a recent paper, Chen and Solis investigated the appearance of spurious solutions when first-order ODEs are discretized using Runge–Kutta schemes. They concluded that the reliability of the numerical solutions to a particular ODE could be verified only by constructing several discrete models and comparing their numerical results with the known properties of the exact solutions. We demonstrate that by using nonstandard schemes, all the difficulties found by Chen and Solis can be eliminated, and that qualitatively correct numerical solutions are obtained for all values of the step size. We illustrate these issues by applying nonstandard finite-difference techniques to the logistic, sine, cubic, and Monod equations.
ISSN:0377-0427
1879-1778
DOI:10.1016/S0377-0427(99)00233-2