[KSCI] Korea Science Citation Index Service

NUMERICAL METHOD FOR SINGULAR PERTURBATION PROBLEMS ARISING IN CHEMICAL REACTOR THEORY

Andargie, Awoke (Department of Mathematics, Bahir dar University)

Publication Information

Journal of applied mathematics & informatics / v.28, no.1_2, 2010 , pp. 411-423 More about this Journal

Abstract

In this paper, a numerical method for singular perturbation problems arising in chemical reactor theory for general singularly perturbed two point boundary value problems with boundary layer at one end(left or right) of the underlying interval is presented. The original second order differential equation is replaced by an approximate first order differential equation with a small deviating argument. By using the trapezoidal formula we obtain a three term recurrence relation, which is solved using Thomas Algorithm. To demonstrate the applicability of the method, we have solved four linear (two left and two right end boundary layer) and one nonlinear problems. From the results, it is observed that the present method approximates the exact or the asymptotic expansion solution very well.

Keywords

Singular perturbations; two point boundary value problems; boundary layer; mixed boundary condition;

Citations & Related Records

Reference

1	A.H. Nayfeh, Introduction to Perturbation Techniques, Wiley, New York,1981.
2	A.H. Nayfeh, Perturbation Methods, Wiley, New York, 1979.
3	. R.E.O'MaUey, Introduction to Singular Perturbations, Academic Press, New York, 1974.
4	Dyk. M. Van Perturbation Methods in Fluid Mechanics, Academic Press, New York, 1964.
5	C.M. Bender, S.A. Orsazag, Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill, New York,1978.
6	F.W. Dorr, S.V. Parter, L.F. Shampine Application of the maximum principal to singular perturbation problems, SIAM review, 5 (1973), 43-88.
7	J. Kevorkian, J.D. Cole, Perturbation Methods in Applied Mathematics, Springer-Verlag, New York, 1981.
8	L.E.El'sgol'ts, S.B, Norkin Introduction to the Theory and Application of Differential Equations with Deviating Arguments, Academic Press, New York, 1973.
9	M.K. Kadalabajoo, Y. N. Reddy, Asymptotic and Numerical analysis of Singular Perturbation Problems, Applied Mathematics and Computation, 30 (1989), 223-259. DOI ScienceOn
10	M.K. Kadalbajoo, K.C. Patidar, A Survey of numerical techniques for solving Singularly perturbed ordinary differential equations, Applied Mathematics and Computation, 130 (2002), 457-510. DOI ScienceOn