scholarly journals On non-standard finite difference models of reaction–diffusion equations

2005 ◽  
Vol 175 (1) ◽  
pp. 11-29 ◽  
Author(s):  
R. Anguelov ◽  
P. Kama ◽  
J.M.-S. Lubuma
Keyword(s):  
Finite Difference ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations

scholarly journals A New Approach and Solution Technique to Solve Time Fractional Nonlinear Reaction-Diffusion Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Inci Cilingir Sungu ◽  
Huseyin Demir
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Time Stepping ◽  
Nonlinear Reaction ◽  
Differential Transform ◽  
Generalized Differential

A new application of the hybrid generalized differential transform and finite difference method is proposed by solving time fractional nonlinear reaction-diffusion equations. This method is a combination of the multi-time-stepping temporal generalized differential transform and the spatial finite difference methods. The procedure first converts the time-evolutionary equations into Poisson equations which are then solved using the central difference method. The temporal differential transform method as used in the paper takes care of stability and the finite difference method on the resulting equation results in a system of diagonally dominant linear algebraic equations. The Gauss-Seidel iterative procedure then used to solve the linear system thus has assured convergence. To have optimized convergence rate, numerical experiments were done by using a combination of factors involving multi-time-stepping, spatial step size, and degree of the polynomial fit in time. It is shown that the hybrid technique is reliable, accurate, and easy to apply.

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