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Abstract : |
Abstract. We discuss the integration of autonomous initial value problems via dynamical rescaling of the vector field (reparameterization of time). A new variant of the leapfrog/Verlet method (adaptive Verlet) enables efficient semi-explicit integration of the reparameterized equations. The method is fairly general (extending to a variety of reparameterization heuristics), retains key features of the true flow such as angular momentum preservation, and can be implemented for the added cost of solving a scalar quartic polynomial equation at each timestep. The use of a step control based on the heuristic of constant streamline density is demonstrated by several numerical experiments, including a double pendulum, the Kepler problem and a three-body problem., |
