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PARAMETER-UNIFORM NUMERICAL METHOD FOR A SYSTEM OF COUPLED SINGULARLY PERTURBED CONVECTION-DIFFUSION EQUATIONS WITH MIXED TYPE BOUNDARY CONDITIONS  

Tamilselvan, A. (Department of Mathematics, School of Mathematical Science, Bharathidasn university)
Ramanujam, N. (Department of Mathematics, School of Mathematics and Computer Science, Bharathidasn University)
Priyadharshini, R. Mythili (Department of Mathematics, School of Mathematics and Computer Science, Bharathidasn University)
Valanarasu, T. (Department of Mathematics, Bharathidasan University College)
Publication Information
Journal of applied mathematics & informatics / v.28, no.1_2, 2010 , pp. 109-130 More about this Journal
Abstract
In this paper, a numerical method for a weakly coupled system of two singularly perturbed convection-diffusion second order ordinary differential equations with the mixed type boundary conditions is presented. Parameter-uniform error bounds for the numerical solution and also to numerical derivative are established. Numerical results are provided to illustrate the theoretical results.
Keywords
Singular perturbation problems; mixed type boundary conditions; Piecewise uniform meshes; Scaled derivative; Scaled discrete derivative;
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1 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 Publishing Co. Pte. Ltd, 1996.
2 A. Tamilselvan, N. Ramanujam and V. Shanthi, A Numerical Method for Singularly Perturbed Weakly Coupled System of Two Second Order Ordinary Differential Equations with Discontinuous Source Term, Journal of computational and applied mathematics, 202 (2007), 203-216.   DOI   ScienceOn
3 R. Mythili Priyadharshini, N. Ramanujam and V. Shanthi, Approximation of Derivative in a System of Singularly Perturbed Convection-Diffusion Equations, Journal of Applied Mathematics and Computation, 29 (2009), 137-151.   DOI   ScienceOn
4 S. Bellew, E. O'Riordan, A Parameter Robust Numerical Method for a System of Two Singularly Perturbed Convection-Diffusion Equations, Applied Numerical Mathematics, 51 (2-3) (2004), 171-186.   DOI   ScienceOn
5 Z. Cen, Parameter- Uniform Finite Difference Scheme for a Sνstem of Coupled Singularly Perturbed Convection-Diffusion Equations, Int. J. Comput. Math., 82 (2) (2005), 177-192.   DOI   ScienceOn
6 Z. Cen, Parameter- Uniform Finite Difference Scheme for a System of Coupled Singularly Perturbed Convection-Diffusion Equations, J. Syst. Sci. Coplex., 18(4) (2005),498-510.
7 Torsten LinB, On System of Singularly Perturbed Reaction-Convection- Diffusion Equations, Preprint MATH- NM-10-2006, TU Dresden, July 2006.
8 N. Madden, M. Stynes, A uniform Convergent Numerical Method for a Coupled System of Two Singularly Perturbed Linear Reaction-Diffusion Problem, IMA Journal of Numerical Analysis, 23(4) (2003), 627-644.   DOI   ScienceOn
9 T. Valanarasu, N. Ramanujam, An Asymptotic Initial Value Method for Boundary Value Problems for a System of Singularly Perturbed Second Ordinary Differential Equations, Applied Mathematics and Computation, 147 (2004), 227-240.   DOI   ScienceOn
10 P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin, Robust Computational Techniques for Boundary Layers, Chapman and Hall/CRC, Boca Ration, 2000.
11 R. Mythili Priyadharshini, N. Ramanujam, Approximation of Derivative to a Singularly Perturbed Second-Order Ordinary Differential Equation with Discontinuous Convection Coefficient using Hybrid Difference Scheme, International Journal of Computer Mathematics, 86 (8) (2009), 1355-1369.   DOI   ScienceOn
12 Ali R. Ansari, A.F. Hegarty, Numerical Solution of a Convection Diffusion Problem with Robin boundary conditions, Journal of Computational and Applied Mathematics, 156(2003), 221-238.   DOI   ScienceOn
13 S. Matthews, Parmeter Robust Numerical Methods for a System of Two copled Singularly Perturbed Reaction-Diffusion Equations, Master's Thesis, School of Mathematics Sciences, Dublin City University, March 2000.
14 E.P. Doolan, J.J.H. Miller, W.H.A. Schilders, Uniform Numerical Methods for Problems with Initial and Boundary Layers, Boole Press, Dublin, 1980.
15 H.G. Roos, M. Stynes, L. Tobiska, Numercal Methods for Singularly Perturbed Differetial Equations, Springer-Verlag, Berlin Heidelberg, 1996.
16 Torsten LinB, Analysis of an Upwind Finite Difference Scheme for a System of Coupled Singularly Perturbed Convection-Diffusion Equations, Equations, Preprint MATH- NM-08-2006, TU Dresden, July 2006.
17 N. Kopteva, M. Stynes, Approximation of Derivatives in a Convection-Diffusion Two-Point Bondary Value Problem, Applied Numerical Mathematics, 39(1) (2001), 47-60.   DOI   ScienceOn