A ROBUST COMPUTATIONAL TECHNIQUE FOR A SYSTEM OF SINGULARLY PERTURBED CONVECTION-DIFFUSION EQUATIONS

2013 ◽  
Vol 10 (05) ◽  
pp. 1350027
Author(s):  
VINOD KUMAR ◽  
R. K. BAWA ◽  
A. K. LAL
Keyword(s):  
Perturbation Parameter ◽  
Shishkin Mesh ◽  
Singularly Perturbed ◽  
Computational Technique ◽  
Singularly Perturbed System ◽  
Initial Value ◽  
Convection Diffusion ◽  
Perturbed System ◽  
Uniformly Convergent ◽  
Theoretical Results

In this paper, a singularly perturbed system of convection-diffusion boundary value problem (BVP) is examined. To solve such type of problem, a modified initial value technique (MIVT) is proposed on an appropriate piecewise uniform Shishkin mesh. The MIVT is shown to be uniformly convergent with respect to the perturbation parameter. Numerical results are presented which are in agreement with the theoretical results.

scholarly journals A robust computational technique for a system of singularly perturbed reaction–diffusion equations

2014 ◽  
Vol 24 (2) ◽  
pp. 387-395
Author(s):  
Vinod Kumar ◽  
Rajesh K. Bawa ◽  
Arvind K. Lal
Keyword(s):  
Reaction Diffusion ◽  
Shishkin Mesh ◽  
Reaction Diffusion Equations ◽  
Singularly Perturbed ◽  
Computational Technique ◽  
Singularly Perturbed System ◽  
Initial Value ◽  
Logarithmic Factor ◽  
Perturbed System ◽  
Theoretical Results

Abstract In this paper, a singularly perturbed system of reaction–diffusion Boundary Value Problems (BVPs) is examined. To solve such a type of problems, a Modified Initial Value Technique (MIVT) is proposed on an appropriate piecewise uniform Shishkin mesh. The MIVT is shown to be of second order convergent (up to a logarithmic factor). Numerical results are presented which are in agreement with the theoretical results.

scholarly journals A finite difference method on layer-adapted mesh for singularly perturbed delay differential equations

2020 ◽  
Vol 5 (1) ◽  
pp. 425-436 ◽  
Author(s):  
Fevzi Erdogan ◽  
Mehmet Giyas Sakar ◽  
Onur Saldır
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Delay Differential Equations ◽  
Perturbation Parameter ◽  
Shishkin Mesh ◽  
Singularly Perturbed ◽  
Initial Value ◽  
Uniformly Convergent ◽  
Delay Differential

AbstractThe purpose of this paper is to present a uniform finite difference method for numerical solution of a initial value problem for semilinear second order singularly perturbed delay differential equation. A numerical method is constructed for this problem which involves appropriate piecewise-uniform Shishkin mesh on each time subinterval. The method is shown to uniformly convergent with respect to the perturbation parameter. A numerical experiment illustrate in practice the result of convergence proved theoretically.

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