Extending nonstandard finite difference schemes rules to systems of nonlinear ODEs with constant coefficients

TL;DR

This paper reformulates Mickens' NSFD rules for systems of ODEs, achieving exact solutions for linear cases and improved accuracy for nonlinear systems through correction terms.

Contribution

It extends Mickens' NSFD rules to systems of ODEs, providing exact schemes for linear cases and enhanced nonlinear schemes with correction terms.

Findings

Exact schemes for linear systems

Improved accuracy in nonlinear systems

Addition of correction terms for Hamiltonian systems

Abstract

In this paper, we present a reformulation of Mickens' rules for nonstandard finite difference (NSFD) scheme to adapt them to systems of ODEs. This leads to exact schemes in the linear case, and also improve the accuracy in the nonlinear case. In the Hamiltonian nonlinear case, it consists in adding correction terms to schemes derived by Mickens.