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.
Highlights
Linear multistep methods (LMMs) are very popular for solving first-order initial value problems (IVPS)
The general k-step method or LMM of step number k is as given in Lambert (1973)
The resulting k-step LMM is of the form: SPECIFICATION OF THE METHOD Let
Summary
A four-point fully implicit method for the numerical integration of third-order ordinary differential equations. 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
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