A Technique to Improve the Error Propagation when Integrating Relative Equilibria

Abstract

We study and perform a way to improve the propagation of errors in the numerical integration of relative equilibria solutions of Hamiltonian differential equations with symmetries. It is well known that in this case and for stable equilibria, the error growth is typically quadratic for ‘general’ schemes and linear for schemes that preserve the invariant quantities of the problem. Here we present a technique to construct methods whose error propagation in time integration of stable relative equilibria is bounded. Numerical results are presented.