American Journal of Applied Mathematics and Statistics
ISSN (Print): 2328-7306 ISSN (Online): 2328-7292 Website: http://www.sciepub.com/journal/ajams Editor-in-chief: Mohamed Seddeek
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American Journal of Applied Mathematics and Statistics. 2015, 3(6), 220-225
DOI: 10.12691/ajams-3-6-2
Open AccessArticle

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

T. Aboiyar.1, T. Luga.1 and B.V. Iyorter2,

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

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

Pub. Date: October 30, 2015

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

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