Extra Derivative Implicit Block Methods for Integrating General Second Order Initial Value Problems

Abstract

This paper focuses on the construction of two-point and three-point implicit block methods for solving general second order Initial Value Problems. The proposed methods are formulated using Hermite Interpolating Polynomial. The block methods approximate the numerical solutions at more than one point at a time directly without reducing the equation into the first order system of ordinary differential equations. In the derivation of the method, the higher derivative of the problem is incorporated into the formula to enhance the efficiency of the proposed methods. The order and zero- stability of the methods are also presented. Numerical results presented show the efficiency of these methods compared to the existing block methods.