A numerical approach for nonsmooth ordinary differential equations

Abstract

In this paper, the authors proposed an approach for solving nonsmooth continuous and discontinuous ordinary differential equations which is based on a generalization of the Taylor expansion. First is considered a generalized derivative for nonsmooth functions with a single variable which is proposed by Kamyad et al. Then, the generalized Taylor expansion of nonsmooth functions is introduced and used to state an approach. Finally, some numerical examples of nonsmooth ordinary differential equations are solved.