Derivation of Continuous Linear Multistep Methods Using Hermite Polynomials as Basis Functions

T. Aboiyar.¹, T. Luga.¹ and B.V. Iyorter^2,

¹Department of Mathematics/Statistics/Computer Science, University of Agriculture, Makurdi, Nigeria

²Department of Mathematics and Computer Science, University of Mkar, Mkar, Nigeria

Cite this paper

T. Aboiyar., T. Luga. and B.V. Iyorter. Derivation of Continuous Linear Multistep Methods Using Hermite Polynomials as Basis Functions. American Journal of Applied Mathematics and Statistics. 2015; 3(6):220-225. doi: 10.12691/AJAMS-3-6-2

Abstract

This paper concerns the derivation of continuous linear multistep methods for solving first-order initial value problems (IVPs) of ordinary differential equations (ODEs) with step number k=3 using Hermite polynomials as basis functions. Adams-Bashforth, Adams-Moulton and optimal order methods are derived through collocation and interpolation technique. The derived methods are applied to solve two first order initial value problems of ordinary differential equations. The result obtained by the optimal order method compared favourably with those of the standard existing methods of Adams-Bashforth and Adams-Moulton.

Keywords

linear multistep method, hermite polynomial, collocation, interpolation, optimal order scheme, ordinary differential equation, initial value problem

Copyright

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