ITA RAS, St-Petersburg, Russia
An efficient procedure was elaborated for high accurate integration of ordinary differential equation systems with nonregular right-hand sides by using the Chebyshev truncated series and a step-size control. This integrator is successfully applied for taking into account the solar pressure in problems of satellite dynamics. Characteristics of numerical integration are investigated on a model, simulating the disturbing motion of LAGEOS, passing through the Earth shadow. Detail analysis of approximation function behavior inside an integration step allows to develop a special algorithm for optimal subdividing an integration step in a gap vicinity. This algorithm is based on the Chebyshev approximation property to reach the maximum error in discontinuity points. The advantages of this technique are demonstrated in comparison to some widely applied integrators. The high effectiveness of this approach is revealed by a number of numerical tests.