IJPAM: Volume 57, No. 4 (2009)

PARAMETER-UNIFORM RITZ-GALERKIN FINITE ELEMENT
METHOD FOR SINGULARLY PERTURBED DELAY
DIFFERENTIAL EQUATIONS WITH DELAY
IN CONVECTION TERM

Arjun Singh Yadaw$^1$, Mohan K. Kadalbajoo$^2$
$^1$Department of Numerical Analysis
Centre of Mathematical Sciences
Lund University
P.O. Box 118, SE-221 00 Lund, SWEDEN
e-mail: arjun@maths.lth.se
$^2$Department of Mathematics and Statistics
Indian Institute of Technology - Kanpur
Kanpur, 208016, INDIA
e-mail: kadal@iitk.ac.in


Abstract.In this paper, we have presented a Ritz-Galerkin finite element method for solving a class of singularly perturbed delay differential equation with small delay in convection term. We have taken a Shishkin mesh to resolve the boundary layer and used hat functions as a basis function for the given method which leads to a tri-digonal linear system. We prove that the method is almost second order convergent independently of the perturbation parameters. Numerical experiments support these theoretical results.

Received: October 11, 2009

AMS Subject Classification: 34K26, 76N20, 65L10, 65M60

Key Words and Phrases: singularly perturbed, boundary layer, second order ODEs, Shishkin mesh, delay differential equation, two point boundary value problems, Ritz-Galerkin finite element method

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 57
Issue: 4