Showing papers by "G. R. W. Quispel published in 2000"
TL;DR: In this article, the authors prove a sufficient condition for Runge-Kutta methods to have the appropriate contraction property for these two-dimensional systems; the midpoint rule is an example.
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TL;DR: In this article, the authors studied the performance of a symplectic numerical integrator based on the splitting method, which is applied to a subtle problem i.e. higher order resonance of the elastic pendulum.
Abstract: In this paper we study the performance of a symplectic numerical integrator based on the splitting method. This method is applied to a subtle problem i.e. higher order resonance of the elastic pendulum. In order to numerically study the phase space of the elastic pendulum at higher order resonance, a numerical integrator which preserves qualitative features after long integration times is needed. We show by means of an example that our symplectic method offers a relatively cheap and accurate numerical integrator.