Numerical methods for non conservative perturbations of conservative problems
In this paper the numerical integration of non conservative perturbations of differential systems that possess a first integral, as for example slowly dissipative Hamiltonian systems, is considered. Numerical methods that are able to reproduce appropriately the evolution of the first integral are proposed. These algorithms are based on a combination of standard numerical integration methods and certain projection techniques. Some conditions under which known conservative methods reproduce that desirable evolution in the invariant are analysed. Finally, some numerical experiments in which we compare the behaviour of the new proposed methods, the averaged vector field method AVF proposed by Quispel and McLaren and standard RK methods of orders 3 and 5 are presented. The results confirm the theory and show a good qualitative and quantitative performance of the new projection methods.
projection methods initial value problems numerical geometric integration dissipative systems non conservative perturbed systems explicit rungekutta methods