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

다국어 초록 (Multilingual 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.

참고문헌 (Reference)

1 E.P. Doolan, "Uniform Numerical Methods for Problems with Initial and Boundary Layers" Boole Press 1980

2 P.A. Farrell, "Robust Computational Techniques for Boundary Layers" Chapman and Hall/CRC 2000

3 S. Matthews, "Parmeter Robust Numerical Methods for a System of Two coupled Singularly Perturbed Reaction-Diffusion Equations" Dublin City University 2000

4 Z. Cen, "Parameter-Uniform Finite Difference Scheme for a System of Coupled SingularlyPerturbed Convection-Diffusion Equations" 82 (82): 177-192, 2005

5 Z. Cen, "Parameter-Uniform Finite Difference Scheme for a System of Coupled Singularly Perturbed Convection-Diffusion Equations" 18 (18): 498-510, 2005

6 Torsten Linß, "On System of Singularly Perturbed Reaction-Convection-Diffusion Equations" TU Dresden 2006

7 Ali R. Ansari, "Numerical Solution of a Convection Diffusion Problem with Robin boundary conditions" (156) : 221-238, 2003

8 H.G. Roos, "Numerical Methods for Singularly Perturbed Differential Equations" Springer-Verlag 1996

9 J.J.H. Miller, "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

10 N. Kopteva, "Approximation of Derivatives in a Convection-Diffusion Two- Point Bondary Value Problem" 39 (39): 47-60, 2001

11 R. Mythili Priyadharshini, "Approximation of Derivative to a Singularly Perturbed Second-Order Ordinary Differential Equation with Discontinuous Convection Coefficient using Hybrid Difference Scheme" 86 (86): 1355-1369, 2009

12 R. Mythili Priyadharshini, "Approximation of Derivative in a System of Singularly Perturbed Convection-Diffusion Equations" (29) : 137-151, 2009

13 Torsten Linß, "Analysis of an Upwind Finite Difference Scheme for a System of Coupled Singularly Perturbed Convection-Diffusion Equations" TU Dresden 2006

14 T. Valanarasu, "An Asymptotic Initial Value Method for Boundary Value Problems for a System of Singularly Perturbed Second Order Ordinary Differential Equations" (147) : 227-240, 2004

15 N. Madden, "A uniform Convergent Numerical Method for a Coupled System of Two Singularly Perturbed Linear Reaction-Diffusion Problem" 23 (23): 627-644, 2003

16 S. Bellew, "A Parameter Robust Numerical Method for a System of Two Singularly Perturbed Convection-Diffusion Equations" 51 (51): 171-186, 2004

17 A. Tamilselvan, "A Numerical Method for Singularly Perturbed Weakly Coupled System of Two Second Order Ordinary Differential Equations with Discontinuous Source Term" (202) : 203-216, 2007