Modified Hybrid Method with Four Stages for Second Order Ordinary Differential Equations

Abstract

A modified explicit hybrid method with four stages is presented, with the first stage exactly integrating exp(wx), while the remaining stages exactly integrate sin(wx) and cos(wx). Special attention is paid to the phase properties of the method during the process of parameter selection. Numerical comparisons of the proposed and existing hybrid methods for several second-order problems show that the proposed method gives high accuracy in solving the Duffing equation and Kramarz’s system.