On a class of four-step modified backward differentiation formula (MBDF) for solving second-order ordinary differential equations

Abstract

This research was conducted to study a class of four-step modified backward differentiation formula (MBDF) for solving second-order ordinary differential equations, with one super-future point. A block method was constructed for the solution of problems of second-order ordinary differential equations. Adopting a step-number, k=4, we obtained a number of discrete methods in block. The stability properties of the block method were investigated using Maple application. In order to ascertain its suitability, the method was tested on some initial valued problems of second-order ordinary differential equations. The numerical solutions of the problems were compared with the respective exact solutions and of other existing methods, and are presented in both tables and graphs.