Variable stepsize stِrmer-cowell methods

Stِrmer and Cowell methods are multistep codes for the numerical solution of second-order initial value problems where the first derivative does not appear explicitly. In this paper, we develop a procedure to obtain k-step Stِrmer and Cowell methods in their variable step size version, avoiding computation of the coefficients by recurrences or integrals. We offer a strategy for conveniently selecting the stepsize. Considering a pair of explicit and implicit formulae, these may be implemented in a predictor-corrector mode.