scholarly journals A Numerical Study on One-Dimensional Reaction-Diffusion Equation and Fisher’s Equation

2020 ◽  
Vol 4 (4) ◽  
pp. 137-146
Author(s):  
Faria Ahmed Shami ◽  
Laek Sazzad Andallah
Keyword(s):  
Diffusion Equation ◽  
Numerical Study ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
One Dimensional ◽  
Fisher’S Equation ◽  
Fisher's Equation

scholarly journals Numerical Solution of Fisher’s Equation Using Finite Difference

2015 ◽  
Vol 12 ◽  
pp. 27-34
Author(s):  
Sharefa Eisa Ali Alhazmi
Keyword(s):  
Nonlinear System ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Diffusion Equation ◽  
Numerical Solution ◽  
Difference Method ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Fisher’S Equation ◽  
Fisher's Equation

A numerical method is proposed to approximate the numeric solutions of nonlinear Fisher’s reaction diffusion equation with finite difference method. The method is based on replacing each terms in the Fisher’s equation using finite difference method. The proposed method has the advantage of reducing the problem to a nonlinear system, which will be derived and solved using Newton method. FTCS and CN method will be introduced, compared and tested.

scholarly journals A reaction-diffusion equation on a thin L-shaped domain

1995 ◽  
Vol 125 (2) ◽  
pp. 283-327 ◽  
Author(s):  
Jack K. Hale ◽  
Geneviève Raugel
Keyword(s):  
Diffusion Equation ◽  
Lower Semicontinuity ◽  
Upper Semicontinuity ◽  
Reaction Diffusion ◽  
Global Attractors ◽  
Reaction Diffusion Equation ◽  
Limit Equation ◽  
One Dimensional ◽  
Shaped Domain

We consider a dissipative reaction–diffusion equation on a thin L-shaped domain (with the thinness measured by a parameter ε); we determine the limit equation for ε = 0 and prove the upper semicontinuity of the global attractors at ε = 0. We also state a lower semicontinuity result. When the limit equation is one-dimensional, we prove convergence of any orbit to a singleton.

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