Modification of the Richardson-Panovsky methods for precise integration of satellite orbits

A family of implicit methods based on intrastep Chebyshev interpolation has been developed to integrate initial value problems of the second-order harmonic oscillator form . The procedure integrates the homogeneous part exactly (in the absence of roundoff errors). The Chebyshev approach uses stepsizes that are considerably larger than those typically used in Runge-Kutta or multistep methods. Computational overhead is comparable to that incurred by high-order conventional procedures. Chebyshev interpolation coupled with the iterative nature of the method substantially reduces local errors. Global error propagation rates are also reduced, making these procedures good candidates for use in long-term simulations of perturbed oscillator systems. The procedure is applied to integrations of the KS transformed equations for the oblateness-perturbed orbital motion of an artificial satellite