Bréhier C.-E. Introduction to numerical methods for Ordinary Differential Equations

Pristina, Kosovo, Serbia, 2016. — 48 p.The aims of these lecture notes are the following:
We introduce Euler numerical schemes, and prove existence and uniqueness of solutions of ODEs passing to the limit in a discretized version.
We provide a general theory of one-step integrators, based on the notions of stability and consistency.
We propose some procedures which lead to construction of higher-order methods.
We discuss splitting and composition methods.
We finally focus on qualitative properties of Hamiltonian systems and of their discretizations.