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A UNIFORMLY CONVERGENT NUMERICAL METHOD FOR A WEAKLY COUPLED SYSTEM OF SINGULARLY PERTURBED CONVECTION-DIFFUSION PROBLEMS WITH BOUNDARY AND WEAK INTERIOR LAYERS
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 Title & Authors
A UNIFORMLY CONVERGENT NUMERICAL METHOD FOR A WEAKLY COUPLED SYSTEM OF SINGULARLY PERTURBED CONVECTION-DIFFUSION PROBLEMS WITH BOUNDARY AND WEAK INTERIOR LAYERS
CHAWLA, SHEETAL; RAO, S. CHANDRA SEKHARA;
 
 Abstract
We consider a weakly coupled system of singularly perturbed convection-diffusion equations with discontinuous source term. The diffusion term of each equation is associated with a small positive parameter of different magnitude. Presence of discontinuity and different parameters creates boundary and weak interior layers that overlap and interact. A numerical method is constructed for this problem which involves an appropriate piecewise uniform Shishkin mesh. The numerical approximations are proved to converge to the continuous solutions uniformly with respect to the singular perturbation parameters. Numerical results are presented which illustrates the theoretical results.
 Keywords
Singular perturbation;Weakly coupled system;Discontinuous source term;Uniformly convergent;Shishkin mesh;Interior layers;
 Language
English
 Cited by
1.
A parameter-uniform second order numerical method for a weakly coupled system of singularly perturbed convection–diffusion equations with discontinuous convection coefficients and source terms, Calcolo, 2017, 54, 3, 1027  crossref(new windwow)
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