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

Marc E. Songolo (1, 2) , Brigitte Bidégaray-Fesquet (3)

1 UNILU - Université de Lubumbashi
2 IETR - Institut d'Électronique et des Technologies du numéRique
3 EDP - Equations aux Dérivées Partielles

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.

Mots clés: Ordinary Differential Equations; Matrix exponential; Exact finite difference schemes; Nonstandard finite difference schemes

Domaines: Analyse numérique [math.NA]

Marc E. Songolo, Brigitte Bidégaray-Fesquet. Extending nonstandard finite difference schemes rules to systems of nonlinear ODEs with constant coefficients. Journal of Difference Equations and Applications, 2024, pp.1-26. ⟨10.1080/10236198.2023.2300726⟩. ⟨hal-03283849⟩