Introduction to numerical methods for Ordinary Differential Equations
Résumé
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.