Proficient trigonometrical-fitted two-derivative multistep collocation methods in predictor-corrector approach: Application to perturbed Kepler problem.

An efficient trigonometrical-fitted two-derivative multistep collocation (TF-TDMC) method using Legendre polynomials up to order five as the basis functions, has been developed for solving second-order ordinary differential equations with oscillatory solution effectively. Interpolation method of approximated power series and collocation technique of its second and third derivative are implemented in the construction of the methods. Two-derivative multistep collocation methods are developed in predictor and corrector form with varying collocation and interpolation points.