Continuous Implicit One Step Four-Point Hybrid Block Method for The Solution of Initial Value Problem for Third Order Ordinary Differential Equations

Abstract

This paper focuses on the development of a continuous hybrid method for direct solution of third order initial value problems (IVPs) of ordinary differential equations (ODEs) using power series as the basis function. The approximate solution was interpolated at all grid and off-grid points except at the point of evaluation and the third derivative of the approximate solution was collocated at the grid points to generate a system of linear equations for the determination of the unknown parameters. The derived method was tested for consistency, zero stability, convergence and absolute stability. The method competes effectively when results are compared with those existing in literatures.