A novel multiderivative hybrid method for the numerical treatment of higher order ordinary differential equations

Abstract EN

This work examines the direct solution ofhigher order (second, third and fouith order) initial value problem (IVP) of ordinary differential equations (ODEs) by hybrid method.

The method was derived using collocation and interpolation technique where the use of power series as an approximate solution is considered.

A two step with two off-step hybrid linear multistep method that gives solution to second, third and fouith order initial value problem of 01'dinaiy differential equations is developed.

Bloek method is used to generate tire independent solution at selected gelid and off glide points.

The properties of the method are properly investigated.

The numerical results generated when the new method is applied to higher order ODEs compared favourably with existing methods in tenns of accuracy.

The developed method takes away tire bui'den of developing separate method for the solution of each of second, third and foui'tli order initial value problem of ordinary differential equations.