IJPAM: Volume 120, No. 3 (2018)

Title

ORTHOGONAL BASED ZERO-STABLE NUMERICAL
INTEGRATOR FOR SECOND ORDER IVPs IN ODEs

Authors

E.O. Adeyefa$^1$, R.B. Adeniyi$^2$, A.M. Udoye$^3$, N.O. Odafi$^4$
$^{1,3,4}$Department of Mathematics
Federal University Oye-Ekiti
Oye-Ekiti, Ekiti State, NIGERIA
$^2$Department of Mathematics
University of Ilorin
Ilorin, Kwara State, NIGERIA

Abstract

This paper presents a set of newly constructed polynomials valid in interval [-1, 1] with respect to weight function $w(x) = (1-x^{2})^{2}$. For applicability sake, the polynomials shall be employed as trial function to develop a fast, efficient and reliable block algorithm for the numerical solution of ordinary differential equations with application to second order initial value problems. Collocation and interpolation techniques were adopted for the formulation of self-starting continuous hybrid schemes. Findings from the analysis of the basic properties of the method using appropriate existing theorems show that the developed schemes are consistent, zero-stable and hence convergent. On implementation, the superiority of the scheme over the existing method is established numerically.

History

Received: June 28, 2016
Revised: April 6, 2018
Published: November 25, 2018

AMS Classification, Key Words

AMS Subject Classification:
Key Words and Phrases:

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How to Cite?

DOI: 10.12732/ijpam.v120i3.4 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2018
Volume: 120
Issue: 3
Pages: 329 - 337


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