Stabilita řešičů soustav obyčejných diferenciálních rovnic

Abstract

The main focus of this master's thesis is to evaluate numerical methods for solving specific systems of ordinary differential equations. No less important to us is to research a different view on classical mechanics, that is descibed by Hamiltonian system. These autonomous differential equations show many interesting properties, in the sense of Hamiltonian flow, such as symplecticity and time reversal symmetry. These properties can also be proved for some numerical methods. Leapfrog method is the point of interest here. We show, this method has many similarities with Hamiltonian flow and we apply it in sampling method called Hybrid Monte Carlo. In the last section we conduct numerical experiments.