Fisher Tipi Denklemleri Çözmek İçin Yeni Bir Metod

Abstract

Bu makalede, Fisher tipi denklemleri çözmek için Fourier dönüşüm metodu ve Adomian Ayrıştırma Metoduna bağlı Fourier Adomian ayrıştırma metodunu (FADM) uyguladık. Ayrıca önerilen metodun dogrulugunu göstermek için iki örnek verildi.

Keywords

• Fourier Dönüşüm Metodu
• Fisher Denklem
• Adomian Ayrıştırma Metodu

A New Method for Solving Fisher-Type Equations

Abstract

In this article, we implemented the Fourier Adomian Decomposition Method (FADM) which depends on the Fourier transform method and the Adomian decomposition method to solve Fisher-type equations. Besides, two examples are represented to show the accuracy and validity of the proposed method.

Keywords

• Fourier Transform Method
• Fisher Equation
• Adomian Decomposition Method

References

1. Fisher, R. (1937). The wave of advance of advantageous genes, Annals of eugenics, 7, 355-369.
2. Kolmogorov, A., Petrovsky, L. & Piskunov, N. (1937). An investigation of the diffusion equation combined with an increase in mass and its application to a biological problem, Bull Uni Moscow Ser Int A, 1, 1-26.
3. Ali, A., Humaira, L. & Shah, K. (2018). Analytical solution of general Fisher’s equation by using Laplace Adomian decomposition method, J. Pure Appl. Math, 2, 1-4.
4. Yıldırım, K., Ibis, B. & Bayram, M. (2012) New solutions of the nonlinear Fisher type equations by the reduced differential transform, Nonlinear Sci Lett A, 3, 29-36.
5. Ağırseven, D. & Öziş, T. (2010) An analytical study for Fisher type equations by using homotopy perturbation method, Computers & Mathematics with Applications, 60, 602-609.
6. Bhalekar, S. & Patade, J. (2016) An analytical solution of fishers equation using decomposition method, Am. J. Comput. Appl. Math, 6, 123-127.
7. Zhou, X. (2008) Exp-function method for solving Fisher's equation. InJournal of Physics: Conference Series, 96, 012063.
8. Kudryashov, N. & Zakharchenko, A. (2014). A note on solutions of the generalized Fisher equation, Applied Mathematics Letters, 32, 53-56.

9. Wazwaz, A. & Gorguis, A. (2004) An analytic study of Fisher's equation by using Adomian decomposition method, Applied Mathematics and Computation, 154, 609-620.
10. Aminikhah, H., Mehrdoust, F. & Jamalian, A. (2012) A new efficient method for nonlinear Fisher-type equations, Journal of Applied Mathematics, 1.
11. Boggess, A. & Narcowich, F. (2015) A first course in wavelets with Fourier analysis, John Wiley & Sons.
12. Bracewell, R. (1986) The Fourier transform and its applications, New York: McGraw-Hill, 31999, 267-272.
13. Düz, M., Issa, A. & Avezov, S. (2022) A new computational technique for Fourier transforms by using the Differential transformation method, Bulletin of International Mathematical Virtual Institute, 12 (2), 287-295.