A Single-Step Modified Block Hybrid Method for General Second-Order Ordinary Differential Equations

Abstract

A multistep collocation approach is used to derive a single-step modified block hybrid method (MBHM) of order five for solving general second-order initial-value problems (IVPs) of ordinary differential equations (ODEs). The new method's basic convergence property is established, and its numerical accuracy is demonstrated using numerical examples from the literature. The new method outperforms similar methods in terms of accuracy, earning it a recommendation as a likely candidate for solving general second-order ODEs.