Two Initial Value Problems Approach for Solving Singular Perturbations Problems

DOI: 10.4236/ajcm.2012.23027   PDF   HTML     4,402 Downloads   7,455 Views  


In this paper, we presented an initial value approach for solving singularly perturbed two point boundary value problems with the boundary layer at one end (left or right). By employing asymptotic power series expansion, the given singularly perturbed two-point boundary value problem is replaced by two first order initial value problems. To demonstrate the applicability of the present method three linear and two nonlinear problems with left end boundary layer are considered. It is observed that the present method approximates the exact solution very well.

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A. Andargie and Y. Reddy, "Two Initial Value Problems Approach for Solving Singular Perturbations Problems," American Journal of Computational Mathematics, Vol. 2 No. 3, 2012, pp. 213-216. doi: 10.4236/ajcm.2012.23027.

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The authors declare no conflicts of interest.


[1] A.Awoke, Y.N. Reddy: “The Method of Asymptotic Inner Boundary Condition for Singular Perturbation Problems”, J. Appl. Math. & Informatics Vol. 29(2011), No. 3 - 4, pp. 937 - 948
[2] A.Awoke, Y.N. Reddy: “Terminal Boundary Condition for Singularly Perturbed Two-Point Boundary Value Problems”, Neural, Parallel, and Scientific Computations 16 (2008) 435 - 448
[3] Kadalabajoo M.K. and Y.N. Reddy: “Asymptotic and Numerical analysis of Singular Perturbation Problems”, Applied Mathematics and Computation 30(1989) 223-259. doi:10.1016/0096-3003(89)90054-4
[4] 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:10.1016/S0096-3003(01)00112-6
[5] C.M. Bender, and S.A.Orsazag: “Advanced Mathematical Methods for Scientists and Engineers”, McGraw-Hill, New York, 1978.
[6] J. Kevorkian and J.D. Cole: “Perturbation Methods in Applied Mathematics”, Springer-Verlag, New York, 1981.
[7] A.H. Nayfeh: “Introduction to Perturbation Techniques”, Wiley, New York, 1981.
[8] A.H. Nayfeh: “Perturbation Methods”, Wiley, New York, 1979.
[9] R.E. O’Malley: “Introduction to Singular Perturbations”, Academic Press, New York,1974.
[10] M. Van Dyk: “Perturbation Methods in Fluid Mechanics”. Academic Press, New York, 1964.]
[11] D.R. Smith: “Singular Perturbation Theory – An Introduction with applications”, Cambridge University Press, Cambridge, 1985.
[12] H.J. Reinhardt: Singular Perturbations of difference methods for linear ordinary differential equations, Applicable Anal., 10 (1980), 53-70. doi:10.1080/00036818008839286

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