An Asymptotic-Numerical Method for a Class of Weakly Coupled System of Singularly Perturbed Convection-Diffusion Equations

2019 ◽  
Vol 40 (13) ◽  
pp. 1550-1571
Author(s):  
Aditya Kaushik ◽  
Anil K. Vashishth ◽  
Vijayant Kumar ◽  
Manju Sharma
Keyword(s):  
Numerical Method ◽  
Coupled System ◽  
Singularly Perturbed ◽  
Diffusion Equations ◽  
Convection Diffusion ◽  
Asymptotic Numerical Method ◽  
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.

scholarly journals Solving Systems of Singularly Perturbed Convection Diffusion Problems via Initial Value Method

2020 ◽  
Vol 2020 ◽  
pp. 1-8 ◽  
Author(s):  
Wondwosen Gebeyaw Melesse ◽  
Awoke Andargie Tiruneh ◽  
Getachew Adamu Derese
Keyword(s):  
Approximate Solution ◽  
Coupled System ◽  
Perturbation Parameter ◽  
Singularly Perturbed ◽  
Initial Value ◽  
Convection Diffusion ◽  
Weakly Coupled ◽  
Weakly Coupled System ◽  
The Given ◽  
Diffusion Problems

In this paper, an initial value method for solving a weakly coupled system of two second-order singularly perturbed Convection–diffusion problems exhibiting a boundary layer at one end is proposed. In this approach, the approximate solution for the given problem is obtained by solving, a coupled system of initial value problem (namely, the reduced system), and two decoupled initial value problems (namely, the layer correction problems), which are easily deduced from the given system of equations. Both the reduced system and the layer correction problems are independent of perturbation parameter, ε. These problems are then solved analytically and/or numerically, and those solutions are combined to give an approximate solution to the problem. Further, error estimates are derived and examples are provided to illustrate the method.

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