A four-point fully implicit method for the numerical integration of third-order ordinary differential equations

Abstract

In this paper, we derived a continuous linear multistep method (LMM) with step number k = 4 through collocation and interpolation techniques using power series as basis function for approximate solution. An order-seven scheme is developed which was used to solve the third-order initial value problems (IVPS) in ordinary differential equation without first reducing to a system first-order. Taylor’s series algorithm of the same order was developed to implement our method. The result obtained was compared favourably with existing methods. Key words: Continuous collocation, multistep methods, interpolation, third-order, power series.