A Numerical Method for Singularly Perturbed Second Order Coupled System of Convection–Diffusion Robin Type Boundary Value Problems with Discontinuous Source Term

In this paper, a numerical method for a weakly coupled system of singularly perturbed convection–diffusion second order ordinary differential equations with discontinuous source term subject to Robin type boundary conditions is presented. A fitted mesh method has been used to obtain the difference s...

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Bibliographic Details
Published inInternational journal of applied and computational mathematics Vol. 1; no. 3; pp. 381 - 397
Main Authors Basha, P. Mahabub, Shanthi, V.
Format Journal Article
LanguageEnglish
Published New Delhi Springer India 01.09.2015
Subjects
Applications of Mathematics
Computational Science and Engineering
Mathematical and Computational Physics
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Nuclear Energy
Operations Research/Decision Theory
Original Paper
Theoretical
Fitted mesh method
Shishkin mesh
Singular perturbation problem
MSC 65L 10
Weakly coupled system
Robin boundary conditions
MSC CR G1.7
Discontinuous source term
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Summary:In this paper, a numerical method for a weakly coupled system of singularly perturbed convection–diffusion second order ordinary differential equations with discontinuous source term subject to Robin type boundary conditions is presented. A fitted mesh method has been used to obtain the difference scheme to solve the system of equations on a piecewise uniform Shishkin mesh. An error estimate is derived to show that the method is uniformly convergent with respect to singular perturbation parameter. Numerical results are provided to illustrate the theoretical results.
ISSN:2349-5103
2199-5796
DOI:10.1007/s40819-014-0021-7