A Legendre spectral finite difference method for the solution of non-linear space-time fractional Burger’s–Huxley and reaction-diffusion equation with Atangana–Baleanu derivative

2020 ◽  
Vol 130 ◽  
pp. 109402 ◽  
Author(s):  
Sachin Kumar ◽  
Prashant Pandey
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Diffusion Equation ◽  
Linear Space ◽  
Difference Method ◽  
Reaction Diffusion ◽  
Space Time ◽  
Reaction Diffusion Equation ◽  
Non Linear

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.

The Transport Dynamics Induced by Riesz Potential in Modeling Fractional Reaction–Diffusion-Mechanics System

2017 ◽  
Vol 13 (2) ◽  
Author(s):  
S. Saha Ray
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Numerical Solutions ◽  
Riesz Potential ◽  
Reaction Diffusion ◽  
Implicit Scheme ◽  
Reaction Diffusion Equation ◽  
Convergence Region ◽  
Fractional Reaction

This paper comprises of a finite difference method with implicit scheme for the Riesz fractional reaction–diffusion equation (RFRDE) by utilizing the fractional-centered difference for approximating the Riesz derivative, and consequently, we obtain an implicit scheme which is proved to be convergent and unconditionally stable. Also a novel analytical approximate method has been dealt with namely optimal homotopy asymptotic method (OHAM) to investigate the solution of RFRDE. The numerical solutions of RFRDE obtained by proposed implicit finite difference method have been compared with the solutions of OHAM and also with the exact solutions. The comparative study of the results establishes the accuracy and efficiency of the techniques in solving RFRDE. The proposed OHAM renders a simple and robust way for the controllability and adjustment of the convergence region and is applicable to solve RFRDE.

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