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Rakesh Ranjan
H. S. Prasad



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Rakesh Ranjan
H. S. Prasad


WSEAS Transactions on Mathematics


Print ISSN: 1109-2769
E-ISSN: 2224-2880

Volume 17, 2018

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.


Volume 17, 2018



An Efficient Method of Numerical Integration for a Class of Singularly Perturbed Two Point Boundary Value Problems

AUTHORS: Rakesh Ranjan, H. S. Prasad

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KEYWORDS: Singular perturbation problems, Bounary value problems, Stability and convergence, Numerical Integration

REFERENCES:

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[2] C. M. Bender, S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill– New York 1978.

[3] P. P. Chakravarthy, S. D. Kumar, R. N. Rao, An exponentially fitted finite difference scheme for a class of singularly perturbed delay differential equations with large delays, Ain Shams Engineering Journal, xxx, 2015, pp. xxx-xxx.

[4] 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.

[5] R. R. Gold, Magnetohydrodynamic pipe flow, Part I. Journal of Fluid Mechanics, 13, 1962, pp. 505-512.

[6] P. W. Hemker, J. J. H. Miller, Numerical Analysis of Singular Perturbation Problems, Academic Press– New York 1979.

[7] M. K. Kadalbajoo, Y. N. Reddy, Asymptotic, numerical analysis of singular perturbation problems: a survey, Applied Mathematics and Computation, 30, 1989, pp. 223-259.

[8] M. K. Kadalbajoo, Y. N. Reddy, An Approximate Method for Solving a Class of Singular Perturbation Problems, Journal of Mathematical for smaller values of N the tendency of maximum absolute error is becoming uniform is fast with respect to larger values of N. Analysis and Applications, 133, 1988, pp. 306- 323.

[9] M. K. Kadalbajoo, Y.-N. Reddy, Numerical Treatment of Singularly Perturbed Two Point Boundary Value Problems, Applied Mathematics and Computation, 21, 1987, pp. 93-110.

[10] M. K. Kadalbajoo, V. K. Aggarwal, Fitted mesh B-spline collocation method for solving self-adjoint singularly perturbed boundary value problems, Applied Mathematics and Computation, 161, 2005, pp. 973987.

[11] M. K. Kadalbajoo, K. K. Sharma, Parameteruniform fitted mesh method for singularly perturbed delay differential equations with layer behavior, Electronic Transactions on Numerical Analysis, 23, 2006, pp. 180-201.

[12] M. K. Kadalbajoo, P. Arora, B-spline collocation method for the singular-perturbation problem using artificial viscosity, Computers and Mathematics with Applications, 57, 2009, pp. 650-663.

[13] M. K. Kadalbajoo, V. Gupta, A brief survey on numerical methods for solving singularly perturbed problems, Applied Mathematics and Computation, 217, 2010, pp. 3641-3716.

[14] J. Kevorkian, J. D. Cole, Perturbation Methods in Applied Mathematics, Springer– New York 1981.

[15] M. Kumar, A. K. Singh, Singular Perturbation Problems in Nonlinear Elliptic Partial Differential Equations: A Survey, International Journal of Nonlinear Science, 17, 3, 2014, pp. 195-214.

[16] J. J. H. Miller, E. O’Riordan, G. I. Shishkin, Fitted Numerical Methods for Singular Perturbation Problems, Error Estimates in the Maximum Norm for Linear Problems in One and Two Dimensions, World Scientific– Singapore 1996.

[17] J. J. H. Miller, Singular Perturbation Problems in Chemical Physics Analytic and Computational Methods, John Wiley– New York 1997.

[18] A. H. Nayfeh, Perturbation Methods, Wiley– New York 1979.

[19] R. E. O’Malley, Introduction to Singular Perturbations, Academic Press– New York 1974.

[20] R. E. O’Malley, Singular Perturbation Methods for Ordinary Differential Equations, Springer– New York 1991.

[21] H. G. Roos, M. Stynes, L. Tobiska, Numerical Methods for Singularly Perturbed Differential Equations, Springer– Berlin 1996.

[22] H. J. Reinhardt, Singular Perturbations of difference methods for linear ordinary differential equations, Applicable Analysis, 10, 1980, pp. 53-70.

[23] V. Shanthi, N. Ramanujam, S. Natesan, Fitted mesh method for singularly perturbed reactionconvection-diffusion problems with boundary and interior layers, J. Appl. Math. and Computing, 22, 1, 2006, pp. 49-65.

[24] V. Subburayan, N. Ramanujam, Asymptotic Initial Value Technique for singularly perturbed convectiondiffusion delay problems with boundary and weak interior layers, Applied Mathematics Letters, 25, 2012, pp. 2272-2278

WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 17, 2018, Art. #33, pp. 265-273


Copyright Β© 2018 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution License 4.0

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