Adaptive Numerical Methods for Solving the Problem about Scattering on a Force Center

Abstract

We construct families of adaptive symplectic conservative numerical methods for solving problems about scattering on a force center. The methods preserve the global properties of the exact solution of the problem and approximate the dependences of the phase variables on time with the second, fourth, or sixth approximation order. The variable time step is selected automatically in two different ways depending on the properties of the solution.