Development of an Order (k+3) Block-Hybrid Linear Multistep Method for the Direct Solution of General Second Order Initial Value Problems

Abstract

Block hybrid linear multistep method was proposed to overcome the Dahlquist order barrier for linear multistep methods. We are interested in answering questions relating to the convergence, accuracy and effectiveness of block hybrid method when utilized to solve Initial Value Problems. In this research work, we presented an order (k+3) block hybrid method for the direct solution of initial value problems of ordinary differential equations. The zero stability, consistency, convergence and the accuracy of the method are improved by collocating and interpolating the power series at finely selected off-grid points. To illustrate the accuracy and effciency of the proposed method, linear and system of initial value problems are considered and the results obtained are compared with the existing methods in literature.