Solving Second-Order IVPs Using an Adaptive Optimized Runge-Kutta-Nyström Method

In this study, an adaptive optimized one-step block Nyström method for solving second-order initial value problems (IVPs) of ODEs is proposed. The new strategy is constructed through a collocation approach with a new technique for choosing the collocation points. The theoretical analysis of the new method is addressed. An embedding-like procedure is considered to estimate the error in order to implement an accurate variable step-size strategy. The numerical tests show that the developed error estimation and the step-size control strategy have good performance compared with other schemes available in the literature