Direct Solution of Second Order Ordinary Differential Equations Using a One-Step Hybrid Block Method

Abstract

In this paper, a one-step block method of order 3 is presented for the direct solution of the general second order ordinary differential equations (ODEs). The continuous formulation of the method was generated through the idea of the collocation and interpolation of the power series approximate solution. As a one-step method, the block method enjoys the desirable properties of the one step methods. The main properties of the method like the order, consistency and zero-stability were all examined in block form. The block method was found to be convergent as it is both consistent and zero-stable. The accuracy of the block method was tested on 3 second order ODEs and results obtained were compared with some existing methods in the literature.