A Single Step Block Numerical Integrator for Direct Solution of Initial Value Problems of Third Order Ordinary Differential Equations

Abstract

This article discusses a single step block numerical integrator for direct solution of initial value problems of third order ordinary differential equations. The derivation of the method is achieved via interpolation and collocation where approximated power series is assigned to be interpolating polynomial. The third derivative of this polynomial is taken as the collocating equations. These interpolating and collocating equations are then put together in a matrix form in order to find the unknown variables which are substituted into the interpolating polynomial to give the continuous implicit scheme. The discrete schemes and its derivatives that form the block are derived by evaluating the continuous implicit scheme as well as its derivatives at the non-interpolating points. The method is found to be order six, zero stable, consistent and also satisfies conditions for convergence. The potency of the method is tested on some third order initial value problems and the outcome proved its effectiveness over current existing methods.