A New Method for Solving Singularly Perturbed Boundary Value Problems

Authors

Essam R. El-Zahar, Department of Mathematics, Faculty of Science and Humanity Studies, Salman Bin AbdulAziz University, Alkharj, KSAFollow
Saber M. M. EL-Kabeir

Author Country (or Countries)

KSA

Abstract

In this paper, a new initial value method for solving a class of nonlinear singularly perturbed boundary value problems with a boundary layer at one end is proposed. The method is designed for the practicing engineer or applied mathematician who needs a practical tool for these problems (easy to use, modest problem preparation and ready computer implementation). Using singular perturbation analysis the method is distinguished by the following fact: the original problem is replaced by a pair of first order initial value problems; namely, a reduced problem and a boundary layer correction problem. These initial value problems are solved using classical fourth order Runge–Kutta method. Numerical examples are given to illustrate the method. It is observed that the present method approximates the exact solution very well.

Suggested Reviewers

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Recommended Citation

R. El-Zahar, Essam and M. M. EL-Kabeir, Saber (2013) "A New Method for Solving Singularly Perturbed Boundary Value Problems," Applied Mathematics & Information Sciences: Vol. 07: Iss. 3, Article 10.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol07/iss3/10