On generalized 4-step implicit linear multistep method for the numerical solution of second order ordinary differential equations

Abstract

In this article, the numerical solutions of Initial Value Problems (IVPs) of general second order Ordinary Differential Equations have been studied. Continuous implicit block 4 step method for solving this type of problem has been developed through the idea of Taylor’s expansion. The main scheme obtained was implemented together with the block formula for the numerical solutions of second order ordinary differential equations. Numerical example was presented to illustrate the applicability and efficiency of the method. The result obtained when compared with exact solution and existing method are favourable.