Introduction to numerical methods for Ordinary Differential Equations

Charles-Edouard Bréhier (1, 2)

1 ICJ - Institut Camille Jordan
2 PSPM - Probabilités, statistique, physique mathématique

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.

Domaines: Analyse numérique [math.NA]

Charles-Edouard Bréhier. Introduction to numerical methods for Ordinary Differential Equations. Licence. Introduction to numerical methods for Ordinary Differential Equations, Pristina, Kosovo, Serbia. 2016. ⟨cel-01484274⟩