Initial Value Method Extended for General Singular Perturbation Problems

Loka Pavani¹ and Y. N. Reddy^2,

¹Department of Mathematics, Osmania University College For Women, Hyderabad, Telangana, India

²Department of Mathematics, National Institute of Technology, Warangal, Telangana, India

Cite this paper:
Loka Pavani and Y. N. Reddy. Initial Value Method Extended for General Singular Perturbation Problems. American Journal of Numerical Analysis. 2015; 3(1):25-29. doi: 10.12691/ajna-3-1-4

Abstract

In this paper the initial value method is extended for solving singularly perturbed two point boundary value problems with internal and terminal layers. It is distinguished by the following fact: The given singularly perturbed boundary value problem is replaced by two first order initial value problems. These first order problems are solved using Runge Kutta method. Model example for each is solved to demonstrate the applicability of the method.

Keywords:
singular perturbations internal layer two layers initial value method

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References:

[1]	Awoke A.T. Numerical Treatment of a class of singular perturbation problems – Ph. D Thesis, NITW, India, April 2008.
[2]	Bender C. M. and Orszag S.A. Advanced Mathematical Methods for Scientists and Engineers, New York: McGraw-Hill, 1978.
[3]	Kadalbajoo M.K. and Reddy Y.N. An Initial Value Technique for a class of Non-linear Singular Perturbation Problems, Journal of Optimization Theory and Applications. - 1987. - Vol. 53. 395-406.
[4]	Kadalbajoo M.K. and Reddy Y.N. Numerical solution of singular perturbation problems by Terminal Boundary Value Technique, Journal of Optimization Theory and Applications. - 1987. - Vol. 52. - pp. 243-254.
[5]	P.W. Hemker, and J.J.H Miller, (Editors), Numerical Analysis of Singular Perturbation Problems, Academic Press, New York, 1979.
[6]	J. Kevorkian, and J. D. Cole, Perturbation Methods in Applied Mathematics, Springer-Verlag, New York, 1981.
[7]	A.H. Nayfeh, Perturbation Methods, Wiley, New York, 1973.
[8]	R.E. O’Malley, Introduction to Singular Perturbations, Academic Press, New York, 1974.
[9]	Y.N. Reddy, Numerical Treatment of Singularly Perturbed Two Point Boundary Value Problems, Ph.D. thesis, IIT, Kanpur, India, 1986.
[10]	M. Van Dyke, Perturbation Methods in Fluid Mechanics, Academic Press, New York, 1964.