scholarly journals Analytic regularity for a singularly perturbed system of reaction-diffusion equations with multiple scales

2012 ◽  
Vol 39 (2) ◽  
pp. 367-394 ◽  
Author(s):  
J. M. Melenk ◽  
C. Xenophontos ◽  
L. Oberbroeckling
Keyword(s):  
Multiple Scales ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Singularly Perturbed ◽  
Diffusion Equations ◽  
Singularly Perturbed System ◽  
Perturbed System ◽  
Analytic Regularity

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.

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