Numerical Algorithms for Direct Solution of Fourth Order Ordinary Differential Equations

Abstract

This paper examines the derivation of hybrid numerical algorithms with step length(k) of five for solving fourth order initial value problems of ordinary differential equations directly. In developing the methods, interpolation and collocation techniques are considered. Approximated power series is used as interpolating polynomial and its fourth derivative as the collocating equation. These equations are solved using Gaussian-elimination approach in finding the unknown variables aj, j=0,...,10 which are substituted into basis function to give continuous implicit scheme. The discrete schemes and its derivatives that form the block are obtained by evaluating continuous implicit scheme at non-interpolating points. The developed methods are of order seven and the results generated when the methods were applied to fourth order initial value problems compared favourably with existing methods.order initial value problems compared favourably with existing methods.

Keywords

• Interpolation
• Collocation
• Block methods
• Fourth order
• Ordinary differential equations