Hybrid Block Method for Direct Solution of Non-Linear Second Order Initial Value Problems in Ordinary Differential Equations

Abstract

This article presents a linear multistep method using both grid and off-grid points of 3 steps using power series as basis function for finding approximate solution to general second order ordinary differential equations. The method of collocation and interpolation is applied at the various points to obtain a new continuous hybrid block method. The basic properties are established and the method found to be convergent. Some nonlinear problems were solved using the new method and the numerical results proved the efficiency of the method.