Variable order step size method for solving orbital problems with periodic solutions

Existing variable order step size numerical techniques for solving a system of higher-order ordinary differential equations (ODEs) requires direct calculating the integration coefficients at each step change. In this study, a variable order step size is presented for direct solving higher-order orbital equations. The proposed algorithm calculates the integration coefficients only once at the beginning and, if necessary, once at the end. The accuracy of the numerical approximation is validated with well-known orbital differential equations. To reduce computational costs, we obtain the relationship for the predictor-corrector algorithm between integration coefficients of various orders. The efficiency of the proposed method is substantiated by the graphical representation of accuracy at the total evaluation steps.