An efficient numerical method for singular perturbation problems

Authors:
J. Vigo-Aguiar;S. Natesan
Affiliations:
Department of Applied Mathematics, University of Salamanca, Salamanca, Spain;Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati, India
Venue:
Journal of Computational and Applied Mathematics - Special issue on computational and mathematical methods in science and engineering (CMMSE-2004)
Year:
2006

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Abstract

In this paper, we propose a method for the numerical solution of singularly perturbed two-point boundary-value problems (BVPs). First, we develop two schemes to integrate initial-value problem (IVP) for system of two first-order differential equations, and then by using these schemes we solve the BVP. Precisely, we convert the second-order BVP into a system of first-order differential equations, and then apply the numerical schemes to obtain the solution. In order to get an initial condition for the system, we use the asymptotic approximate solution. Error estimates are derived and numerical examples are provided to illustrate the present method.