IJPAM: Volume 41, No. 6 (2007)

THE NUMERICAL SOLUTION OF SINGULARLY
PERTURBED BOUNDARY VALUE PROBLEMS
USING NONPOLYNOMIAL SPLINE

M.A. Ramadan$^1$, I.F. Lashien$^2$, W.K. Zahra$^3$
$^1$Department of Mathematics
Faculty of Science
Menoufia University
Shebeen El-Koom, EGYPT
e-mail: mramadan@mailer.eun.eg
$^{2,3}$Department of Engineering, Physics and Mathematics
Faculty of Engineering
Tanta University
Tanta, EGYPT
$^3$e-mail: waheed_zahra@yahoo.com


Abstract.In this paper, we develop a class of methods for the numerical solution to singularly perturbed boundary value problems (SPBVPs) using nonpolynomial spline. The present approach leads to a generalized scheme that has third-order and fourth-order convergence depending on the choice of the parameters $\alpha$, $\beta $ and $\omega $'s involved in the method. Our scheme leads to a tridiagonal system of linear equations. Convergence analysis of the methods is discussed. Two numerical examples are included to validate the practical usefulness and the superiority of our methods.

Received: November 15, 2007

AMS Subject Classification: 65L10

Key Words and Phrases: nonpolynomial spline, singularly perturbed boundary value problems, monotone matrices, irreducible matrices, convergence analysis

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 41
Issue: 6