eng
Science and Education Publishing
American Journal of Numerical Analysis
2328-7292
2014-08-18
2
4
128
135
10.12691/ajna-2-4-5
AJNA2014245
article
A Domain Decomposition Method for Solving Singularly Perturbed Two Point Boundary Value Problems via Exponential Splines
P. Padmaja
1
Y.N. Reddy
ynreddy_nitw@yahoo.com
2
Department of Mathematics, Prasad V Potluri Siddhartha Institute of Technology, Vijayawada, Andhra Pradesh, INDIA
Department of Mathematics, National Institute of Technology, Warangal, INDIA
In this paper, we presented a domain decomposition method via exponential splines for solving singularly perturbed two-point boundary value problems with the boundary layer at one end (left or right) point. The method is distinguished by the following fact: The original singularly perturbed two-point boundary value problem is divided into two problems, namely inner and outer region problems. The terminal boundary condition is obtained from the solution of the reduced problem. Using stretching transformation, a modified inner region problem is constructed. Then, the inner region problem is solved as two-point boundary value problems by employing exponential splines. Several linear and nonlinear problems are solved to demonstrate the applicability of the method.
http://pubs.sciepub.com/ajna/2/4/5/ajna-2-4-5.pdf
singular perturbation problems
inner region problem
outer region problem
boundary layer
exponential splines