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.
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