Trajectory Propagation Using Information on Periodicity

Families of methods to integrate first and second order ordinary differential equations whose solution known to be periodic will be discussed. The methods can be tuned to a possibly a-priori knowledge of the user on the location of the frequencies, that are dominant in the exact solution. On the basis of such extra information the truncation error can considerably be reduced in magnitude. The paper compares these methods to well known in integrators and discusses a simple mechanism to estimate the frequency during the integration process