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.
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