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 ◽  
Vol 54 (3) ◽  
pp. 1027-1053 ◽  
Author(s):  
Mahabub Basha Pathan ◽  
Shanthi Vembu
Keyword(s):  
Numerical Method ◽  
Coupled System ◽  
Second Order ◽  
Singularly Perturbed ◽  
Diffusion Equations ◽  
Source Terms ◽  
Convection Diffusion ◽  
Weakly Coupled ◽  
Weakly Coupled System

AN ALMOST-SECOND-ORDER METHOD FOR A SYSTEM OF SINGULARLY PERTURBED CONVECTION–DIFFUSION EQUATIONS WITH NONSMOOTH CONVECTION COEFFICIENTS AND SOURCE TERMS

2010 ◽  
Vol 07 (02) ◽  
pp. 261-277 ◽  
Author(s):  
A. TAMILSELVAN ◽  
N. RAMANUJAM
Keyword(s):  
Coupled System ◽  
Second Order ◽  
Singularly Perturbed ◽  
Diffusion Equations ◽  
Source Terms ◽  
Convection Diffusion ◽  
Weakly Coupled ◽  
Weakly Coupled System ◽  
Type Boundary ◽  
Second Order Convergence

In this paper, a weakly coupled system of two singularly perturbed convection–diffusion equations with discontinuous convection coefficients and source terms with Dirichlet type boundary conditions is considered. A hybrid finite difference scheme on a Shishkin mesh generating almost-second-order convergence in the maximum norm is constructed for solving this problem. To illustrate the theoretical results, numerical experiments are performed.

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