Comparison of non-standard finite difference methods for vibro-impact systems
The aim of this paper is to continue our investigation in the application of the non-standard finite difference methods in non-smooth mechanics. We focus our study on $N$-dimensional vibro-impact systems. In particular,
we construct non-standard schemes associated to well known schemes developed and studied by Paoli and Schatzman (called here after the PS-scheme), Moreau, Monteiro-Marques and Mabrouk (called here after the MMM-scheme). We compare them and show that the non-standard MMM-scheme can give spurious numerical solutions, while the non-standard PS-scheme give satisfactory results.