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A New Method for Solving Fisher-Type Equations

Year 2024, Volume: 11 Issue: 2, 270 - 275, 29.11.2024
https://doi.org/10.35193/bseufbd.1315932

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.

References

  • Fisher, R. (1937). The wave of advance of advantageous genes, Annals of eugenics, 7, 355-369.
  • 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.
  • 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.
  • 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.
  • Ağırseven, D. & Öziş, T. (2010) An analytical study for Fisher type equations by using homotopy perturbation method, Computers & Mathematics with Applications, 60, 602-609.
  • Bhalekar, S. & Patade, J. (2016) An analytical solution of fishers equation using decomposition method, Am. J. Comput. Appl. Math, 6, 123-127.
  • Zhou, X. (2008) Exp-function method for solving Fisher's equation. InJournal of Physics: Conference Series, 96, 012063.
  • Kudryashov, N. & Zakharchenko, A. (2014). A note on solutions of the generalized Fisher equation, Applied Mathematics Letters, 32, 53-56.
  • Wazwaz, A. & Gorguis, A. (2004) An analytic study of Fisher's equation by using Adomian decomposition method, Applied Mathematics and Computation, 154, 609-620.
  • Aminikhah, H., Mehrdoust, F. & Jamalian, A. (2012) A new efficient method for nonlinear Fisher-type equations, Journal of Applied Mathematics, 1.
  • Boggess, A. & Narcowich, F. (2015) A first course in wavelets with Fourier analysis, John Wiley & Sons.
  • Bracewell, R. (1986) The Fourier transform and its applications, New York: McGraw-Hill, 31999, 267-272.
  • 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.

Fisher Tipi Denklemleri Çözmek İçin Yeni Bir Metod

Year 2024, Volume: 11 Issue: 2, 270 - 275, 29.11.2024
https://doi.org/10.35193/bseufbd.1315932

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.

References

  • Fisher, R. (1937). The wave of advance of advantageous genes, Annals of eugenics, 7, 355-369.
  • 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.
  • 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.
  • 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.
  • Ağırseven, D. & Öziş, T. (2010) An analytical study for Fisher type equations by using homotopy perturbation method, Computers & Mathematics with Applications, 60, 602-609.
  • Bhalekar, S. & Patade, J. (2016) An analytical solution of fishers equation using decomposition method, Am. J. Comput. Appl. Math, 6, 123-127.
  • Zhou, X. (2008) Exp-function method for solving Fisher's equation. InJournal of Physics: Conference Series, 96, 012063.
  • Kudryashov, N. & Zakharchenko, A. (2014). A note on solutions of the generalized Fisher equation, Applied Mathematics Letters, 32, 53-56.
  • Wazwaz, A. & Gorguis, A. (2004) An analytic study of Fisher's equation by using Adomian decomposition method, Applied Mathematics and Computation, 154, 609-620.
  • Aminikhah, H., Mehrdoust, F. & Jamalian, A. (2012) A new efficient method for nonlinear Fisher-type equations, Journal of Applied Mathematics, 1.
  • Boggess, A. & Narcowich, F. (2015) A first course in wavelets with Fourier analysis, John Wiley & Sons.
  • Bracewell, R. (1986) The Fourier transform and its applications, New York: McGraw-Hill, 31999, 267-272.
  • 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.
There are 13 citations in total.

Details

Primary Language English
Subjects Applied Mathematics (Other)
Journal Section Articles
Authors

Murat Düz 0000-0003-2387-4045

Ahmad Issa 0000-0001-7495-3443

Publication Date November 29, 2024
Submission Date June 17, 2023
Acceptance Date December 16, 2023
Published in Issue Year 2024 Volume: 11 Issue: 2

Cite

APA Düz, M., & Issa, A. (2024). A New Method for Solving Fisher-Type Equations. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi, 11(2), 270-275. https://doi.org/10.35193/bseufbd.1315932