Numerical Solution of Fisher’s Equation Using Finite Difference

Ali Alhazmi, Sharefa Eisa

doi:10.18052/www.scipress.com/BMSA.12.27

BMSA > BMSA Volume 12 > Numerical Solution of Fisher’s Equation Using...

< Back to Volume

Numerical Solution of Fisher’s Equation Using Finite Difference

Full Text PDF

Abstract:

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.

Info:

Periodical:

Bulletin of Mathematical Sciences and Applications (Volume 12)

Pages:

27-34

DOI:

https://doi.org/10.18052/www.scipress.com/BMSA.12.27

Citation:

S. E. Ali Alhazmi, "Numerical Solution of Fisher’s Equation Using Finite Difference", Bulletin of Mathematical Sciences and Applications, Vol. 12, pp. 27-34, 2015

Online since:

May 2015

Authors:

Sharefa Eisa Ali Alhazmi

Keywords:

Crank Nicholson Method, Fisher’s Equation, Forward Time Centered Space, Integral Equation, Non-Linear Diffusion Equation

Export:

RIS, BibTeX, Text

Distribution:

Open Access

This work is licensed under a
Creative Commons Attribution 4.0 International License

References:

R. A. Fisher. The Wave of Advance of Advantageous Genes, Annals of Genetics, Vol. 7, No. 4, 1937, p.353.

A. Kolmogorov, I. Petrovskii and N. Piscounov. Etude de L'quation de la Diffusion Avec Croissance de la Quantit de Matire et Son Application a un Problem Biologique. In: V. M. Tikhomirov, Ed., Selected Works of A. N. Kolmogorov I, Kluwer, Dordrecht, 1991, p.248.

B. H. Gilding and R. Kersner. Travelling Waves in Nonlinear Diffusion Convection Reaction. Birkhuser, Basel, 2004. doi: 10. 1007/978-3-0348-7964-4.

J. D. Murray. Mathematical Biology. Springer-Verlag, New York, (1993).

R. A. Fisher. The wave of advance of advantageous genes. Ann. Eugenics, 7 (1937), 353369.

M.J. Ablowitz and A. Zeppetella. Explicit solution of Fisher's equation for a special wave speed. Bull. Math. Biol., Vol. 41(835), (1979).

D. A. Kopriva. Implementing Spectral Methods for Partial Differential Equations: Algorithms for Scientists and Engineers. Springer, Berlin, Germany, (2009).

C. Canuto M.Y. Hussaini, A. Quarteroni, and T. A. Zang. SpectralMethods: Fundamentals in Single Domains, Springer, Berlin, Germany, (2006).

C. I. Gheorghiu. Spectral Methods for Differential Problems, T. Popoviciu Institute of Numerical Analysis, Cluj-Napoca, Romaina, (2007).

E. H. Doha, W. M. Abd-Elhameed, and A. H. Bhrawy. New spectral-Galerkin algorithms for direct solution of high evenorder differential equations using symmetric generalized Jacobi polynomials. Collectanea Mathematica, vol. 64, no. 3, pp.373-394, (2013).

E.H. Doha and A. H. Bhrawy. An efficient direct solver formultidimensional elliptic Robin boundary value problems using a Legendre spectral-Galerkin method. Computers Mathematics with Applications, vol. 64, no. 4, p.558571, (2012).

A. H. Bhrawy1, 2 andM. A. Alghamdi1. Approximate Solutions of Fisher's Type Equations with Variable Coefficients. Hindawi Publishing Corporation Abstract and Applied Analysis. Volume 2013, Article ID 176730, 10 pages. http: /dx. doi. org/10. 1155/2013/176730.

S. Tang and R.O. Weber. Numerical study of Fisher's equation by a Petrov-Galerkin finite element method, Jour. Austr. Math. Sot. 33, 27-38 (1991).

T. Mavounugou and Y. Cerrault. Numerical study of Fisher's equation by Adomian's method, . Mathl. Comput. Modelling 19 (l), 89-95 (1994).

Zhaosheng Feng. Traveling waves to a reaction diffusion equation. Discrete and continuous website: www. AIMSciences. org. Dynamical systems. p.382390.

Show More Hide

Cited By:

[1] M. MOSTAFA, M. RABAB, F. RAMY, "SOLVING FISHER'S EQUATION USING MODIFIED EXPONENTIAL CUBIC B-SPLINE DIFFERENTIAL QUADRATURE", i-manager’s Journal on Mathematics, Vol. 9, p. 8, 2020

DOI: https://doi.org/10.26634/jmat.9.2.17941