A Numerical Method for a System of Singularly Perturbed Differential Equations of Reaction-Diffusion Type with Negative Shift

2016 ◽  
pp. 99-116
Author(s):  
P. Avudai Selvi ◽  
Ramanujam Narasimhan
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Reaction Diffusion ◽  
Singularly Perturbed ◽  
Diffusion Type ◽  
Negative Shift

A parameter uniform essentially first-order convergent numerical method for a parabolic system of singularly perturbed differential equations of reaction–diffusion type with initial and Robin boundary conditions

2019 ◽  
Vol 12 (01) ◽  
pp. 1950001 ◽  
Author(s):  
R. Ishwariya ◽  
J. J. H. Miller ◽  
S. Valarmathi
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Numerical Method ◽  
Reaction Diffusion ◽  
Singularly Perturbed ◽  
Robin Boundary Conditions ◽  
Diffusion Type ◽  
Parabolic Boundary ◽  
First Order ◽  
Robin Boundary

In this paper, a class of linear parabolic systems of singularly perturbed second-order differential equations of reaction–diffusion type with initial and Robin boundary conditions is considered. The components of the solution [Formula: see text] of this system are smooth, whereas the components of [Formula: see text] exhibit parabolic boundary layers. A numerical method composed of a classical finite difference scheme on a piecewise uniform Shishkin mesh is suggested. This method is proved to be first-order convergent in time and essentially first-order convergent in the space variable in the maximum norm uniformly in the perturbation parameters.

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