scholarly journals Numerical and theoretical treatment based on the compact finite difference and Spectral collocation algorithms of the space fractional-order Fisher's equation

Authorea ◽  
2020 ◽  
Author(s):  
Mohamed Adel ◽  
Mohamed Khader
Keyword(s):  
Finite Difference ◽  
Fractional Order ◽  
Theoretical Treatment ◽  
Spectral Collocation ◽  
Compact Finite Difference ◽  
Fisher’S Equation ◽  
Fisher's Equation

Numerical and theoretical treatment based on the compact finite difference and spectral collocation algorithms of the space fractional-order Fisher’s equation

2020 ◽  
Vol 31 (09) ◽  
pp. 2050122
Author(s):  
M. M. Khader ◽  
M. Adel
Keyword(s):  
Finite Difference ◽  
Fractional Order ◽  
Time Derivative ◽  
Theoretical Treatment ◽  
Algebraic Equations ◽  
Spectral Collocation ◽  
Compact Finite Difference ◽  
Fisher’S Equation ◽  
Fisher's Equation ◽  
Accurate Numerical Algorithm

This paper presents an accurate numerical algorithm to solve the space fractional-order Fisher’s equation where the derivative operator is described in the Caputo derivative sense. In the presented discretization process, first, we use the compact finite difference (CFD) for a semi-discrete occurrence in time derivative and implement the Chebyshev spectral collocation method (CSCM) of the third-kind to discretize the spatial fractional derivative. The presented method converts the problem understudy to be a system of algebraic equations which can be easily solved. To study the convergence and stability analysis, some theorems are given with their proofs. A numerical simulation is outputted to test the accuracy and applicability of our presented algorithm.

scholarly journals LIE SYMMETRY ANALYSIS TO FISHER'S EQUATION WITH TIME FRACTIONAL ORDER

2020 ◽  
Vol 10 (5) ◽  
pp. 2058-2067
Author(s):  
Zhenli Wang ◽  
◽  
Lihua Zhang ◽  
Hanze Liu ◽  
◽  
...  
Keyword(s):  
Fractional Order ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis ◽  
Fisher’S Equation ◽  
Fisher's Equation

A NOTE ON THE LATTICE BOLTZMANN VERSUS FINITE-DIFFERENCE METHODS FOR THE NUMERICAL SOLUTION OF THE FISHER'S EQUATION

2013 ◽  
Vol 25 (01) ◽  
pp. 1340015 ◽  
Author(s):  
SAURO SUCCI
Keyword(s):  
Finite Difference ◽  
Lattice Boltzmann ◽  
Finite Difference Methods ◽  
Difference Schemes ◽  
Diffusion Reaction ◽  
Finite Difference Schemes ◽  
Fisher’S Equation ◽  
Advection Diffusion ◽  
Fisher's Equation ◽  
Better Than

We assess the Lattice Boltzmann (LB) method versus centered finite-difference schemes for the solution of the advection–diffusion–reaction (ADR) Fisher's equation. It is found that the LB method performs significantly better than centered finite-difference schemes, a property we attribute to the near absence of dispersion errors.

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.

A Fully Discrete Spectral Method for Fisher’s Equation on the Whole Line

2016 ◽  
Vol 6 (4) ◽  
pp. 400-415 ◽  
Author(s):  
Yu-Jian Jiao ◽  
Tian-Jun Wang ◽  
Qiong Zhang
Keyword(s):  
Finite Difference ◽  
Theoretical Analysis ◽  
Asymptotic Solution ◽  
Spectral Method ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Fisher’S Equation ◽  
Fully Discrete ◽  
Fisher's Equation ◽  
Solution Behaviour

AbstractA generalised Hermite spectral method for Fisher's equation in genetics with different asymptotic solution behaviour at infinities is proposed, involving a fully discrete scheme using a second order finite difference approximation in the time. The convergence and stability of the scheme are analysed, and some numerical results demonstrate its efficiency and substantiate our theoretical analysis.

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