Parametrization of the Solution of the Kepler Problem and New Adaptive Numerical Methods Based on This Parametrization

Аннотация

We propose a one-parameter family of adaptive numerical methods for solving the Kepler problem. The methods preserve the global properties of the exact solution of the problem and approximate the time dependence of the phase variables with the second or fourth approximation order. The variable time increment is determined automatically from the properties of the solution.