Efficient adaptive step-size formulation of an optimized two-step hybrid block method for directly solving general second-order initial-value problems.

Abstract

[EN]In this article, we have considered an adaptive step-size formulation of an optimized block method for directly solving general second-order initial value problems of ODEs numerically. This formulation has been done using an embedded-type procedure resulting in an efficient method that performs much better compared to its counterpart fixed step-size method and other existing block strategies.