scholarly journals A uniformly convergent method for a singularly perturbed semilinear reaction-diffusion problem with nonunique solutions

1995 ◽  
Vol 0034 ◽  
pp. 47-47
Author(s):  
G. Sun ◽  
M. Stynes
Keyword(s):  
Reaction Diffusion ◽  
Diffusion Problem ◽  
Singularly Perturbed ◽  
Convergent Method ◽  
Uniformly Convergent

scholarly journals A Uniformly Convergent Collocation Method for Singularly Perturbed Delay Parabolic Reaction-Diffusion Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Fasika Wondimu Gelu ◽  
Gemechis File Duressa
Keyword(s):  
Collocation Method ◽  
Reaction Diffusion ◽  
Diffusion Problem ◽  
Euler Method ◽  
Singularly Perturbed ◽  
Uniform Mesh ◽  
Spline Collocation ◽  
Step Size ◽  
Uniformly Convergent ◽  
Type Boundary

In this article, a numerical solution is proposed for singularly perturbed delay parabolic reaction-diffusion problem with mixed-type boundary conditions. The problem is discretized by the implicit Euler method on uniform mesh in time and extended cubic B-spline collocation method on a Shishkin mesh in space. The parameter-uniform convergence of the method is given, and it is shown to be ε -uniformly convergent of O Δ t + N − 2 ln 2 N , where Δ t and N denote the step size in time and number of mesh intervals in space, respectively. The proposed method gives accurate results by choosing suitable value of the free parameter λ . Some numerical results are carried out to support the theory.

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