Parameter‐uniform numerical method for singularly perturbed 2‐D parabolic convection–diffusion problem with interior layers

2021 ◽  
Author(s):  
Anirban Majumdar ◽  
Srinivasan Natesan
Keyword(s):  
Numerical Method ◽  
Diffusion Problem ◽  
Singularly Perturbed ◽  
Convection Diffusion ◽  
Interior Layers

scholarly journals A Numerical Method for a Singularly Perturbed Three-Point Boundary Value Problem

2010 ◽  
Vol 2010 ◽  
pp. 1-17 ◽  
Author(s):  
Musa Çakır ◽  
Gabil M. Amiraliyev
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Numerical Method ◽  
Numerical Experiments ◽  
Diffusion Problem ◽  
Singularly Perturbed ◽  
Point Boundary ◽  
Convection Diffusion ◽  
First Order ◽  
Type Boundary

The purpose of this paper is to present a uniform finite difference method for numerical solution of nonlinear singularly perturbed convection-diffusion problem with nonlocal and third type boundary conditions. The numerical method is constructed on piecewise uniform Shishkin type mesh. The method is shown to be convergent, uniformly in the diffusion parameterε, of first order in the discrete maximum norm. Some numerical experiments illustrate in practice the result of convergence proved theoretically.

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