Abstract
We present an algorithm for the rapid numerical integration of a time-periodic ODE with a small dissipation term that is C1 in the velocity. Such an ODE arises as a model of spin-orbit coupling in a star/planet system, and the motivation for devising a fast algorithm for its solution comes from the desire to estimate probability of capture in various solutions, via Monte Carlo simulation: the integration times are very long, since we are interested in phenomena occurring on timescales of the order of 106{ 107 years. The proposed algorithm is based on the High-order Euler Method (HEM) which was described in [Bartuccelli et al. 2015], and it requires computer algebra to set up the code for its implementation. The pay-o is an overall increase in speed by a factor of about 7:5 compared to standard numerical methods. Means for accelerating the purely numerical computation are also discussed.