A Domain Decomposition Method for Solving Singularly Perturbed Two Point Boundary Value Problems via Exponential Splines

P. Padmaja¹ and Y.N. Reddy^2,

¹Department of Mathematics, Prasad V Potluri Siddhartha Institute of Technology, Vijayawada, Andhra Pradesh, INDIA

²Department of Mathematics, National Institute of Technology, Warangal, INDIA

Cite this paper:
P. Padmaja and Y.N. Reddy. A Domain Decomposition Method for Solving Singularly Perturbed Two Point Boundary Value Problems via Exponential Splines. American Journal of Numerical Analysis. 2014; 2(4):128-135. doi: 10.12691/ajna-2-4-5

Abstract

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.

Keywords:
singular perturbation problems inner region problem outer region problem boundary layer exponential splines

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