DOI QR코드

DOI QR Code

SOLVING THE GENERALIZED FISHER'S EQUATION BY DIFFERENTIAL TRANSFORM METHOD

  • Matinfar, M. (Dep. of Mathematics, University of Mazandaran) ;
  • Bahar, S.R. (Dep. of Mathematics, University of Mazandaran) ;
  • Ghasemi, M. (Dep. of Mathematics, University of Mazandaran)
  • 투고 : 2010.06.24
  • 심사 : 2011.08.30
  • 발행 : 2012.05.30

초록

In this paper, differential transform method (DTM) is considered to obtain solution to the generalized Fisher's equation. This method is easy to apply and because of high level of accuracy can be used to solve other linear and nonlinear problems. Furthermore, is capable of reducing the size of computational work. In the present work, the generalization of the two-dimensional transform method that is based on generalized Taylor's formula is applied to solve the generalized Fisher equation and numerical example demonstrates the accuracy of the present method.

키워드

참고문헌

  1. A.K. Khalifa, K.R. Raslan, H.M. Alzubaidi, Numerical study using the ADM for the modified regularized long wave equation , Appl. Math. Modelling , vol. 32, no. 12, pp. 2962-2972, 2008. https://doi.org/10.1016/j.apm.2007.10.014
  2. S. Abbasbandy, M.T. Darvishi, A numerical solution of Burgers' equation by modified Adomian method, Appl. Math. Comput., vol. 163, pp. 1265-1272, 2005.
  3. S. Momani, Z. Odibat, Analytical solution of a time-fractional NavierStokes equation by Adomian decomposition method, Appl. Math. Comput., vol. 177, pp. 488494, 2006.
  4. Z. Odibat, S. Momani, Application of variational iteration method to nonlinear differential equations of fractional order, Int. J. Non. Sci. Numer. Simul., vol. 7, no. 1, pp. 1527, 2006.
  5. Hakan K. Akmaz, Variational Iteration Method for elastodynamic Green's functions, Non. Analysis. Teory and Applications, vol. 71, no. 12, pp. 218-223, 2009.
  6. D. Altintan, O. Ugur, Variational Iteration Method for Sturm-Lioville differential equations, Compu. and Math. with Application, vol. 58, no. 2, pp. 322-328, 2009. https://doi.org/10.1016/j.camwa.2009.02.029
  7. J.Biazar, H.Ghazvini, Numerical solution for special nonlinear Fredholm integral equation by HPM, Appl. Math. and Compu., vol. 195, no. 2, pp. 681-687, 2008. https://doi.org/10.1016/j.amc.2007.05.015
  8. B. Ganjavi, H. Mohammadi, D. D. Ganji, A. Barari, Homotopy pertubration method and variational iteration method for solving Zakharov-Kuznetsov equation, Am. J. Appl .Sci., vol. 5, no. 7, pp. 811-817, 2008. https://doi.org/10.3844/ajassp.2008.811.817
  9. M. Gorji, D.D. Ganji and S. Soleimani, Homotopy Perturbation Method for solving boundary value problems, Phy. Lett., A, vol. 350, no. 1-2, pp. 87-88, 2006. https://doi.org/10.1016/j.physleta.2005.10.005
  10. N. Bildik, A. Konuralp, F. Bek, S. Kucukarslan, Solution of different type of the partial differential equation by differential transform method and Adomians decomposition method, Appl. Math. Comput., vol. 172, pp. 551567, 2006.
  11. Z. Odibat, S. Momani, A generalized differential transform method for linear partial differential equations of fractional order, App. Math. Lett., vol. 21, pp. 194-199, 2008. https://doi.org/10.1016/j.aml.2007.02.022
  12. J. Biazar, M. Eslami, Differential Transform Method for Quadratic Riccati Differential Equation, Int. J. Non. Sci., vol. 9, no. 4, pp. 444-447, 2010.
  13. J. K. Zhou, Differential Transformation and its Applications for Electrical Circuits, Huzhong Univ. Press, Wuhan, China, 1986.
  14. C. L. Chen, Y. C. Liu, Solution of two point boundary value problems using the differential transformation method, J. Opt. Theory Appl., vol. 99, pp. 23-35, 1998. https://doi.org/10.1023/A:1021791909142
  15. Fatma Ayaz, Applications of differential transform method to to differential-algebraic equations, App. Math. and Compu., vol. 152, pp. 649-657, 2004. https://doi.org/10.1016/S0096-3003(03)00581-2
  16. Figen Kangalgil and Fatma Ayaz, Solitary wave solutions for the KdV and mKdV equations by differential transform method, Chaos Solitons and Fractals, vol.41, no. 1, pp. 464-472, 2009. https://doi.org/10.1016/j.chaos.2008.02.009
  17. S. V. Ravi Kanth, K. Aruna Two-dimensional differential transform method for solving linear and non-linear Schroinger equations, Chaos Solitons and Fractals, vol. 41, no. 5, pp. 2277-2281, 2009. https://doi.org/10.1016/j.chaos.2008.08.037
  18. A. Arikoglu, I. Ozkol, Solution of fractional differential equations by using differential transform method, Chaos Solitons and Fractals, vol. 34, pp. 1473-1481, 2007. https://doi.org/10.1016/j.chaos.2006.09.004
  19. W. Malfliet, Solitary wave solutions of nonlinear wave equations, Am. J. Phys., vol. 7, pp. 650-654, 1992.
  20. P. Brazhnik, J. Tyson, On traveling wave solutions of Fisher's equationin two spatial dimensions, SIAM, J. Appl. Math., vol. 60, no. 2, pp. 371-391, 1999. https://doi.org/10.1137/S0036139997325497
  21. M. Matinfar, M. Ghanbari, The application of the modified variational iteration method on the generalized Fisher's equation, Springer, J. Appl. Math. Comput., vol. 31, pp. 165-175, 2009. https://doi.org/10.1007/s12190-008-0199-0
  22. A.M. Wazwaz, A. Gorguis, An analytic study of Fisher's equation by using Adomian decomposition method, App. Math. and Compu., vol. 154, no. 3, pp. 609620, 2004. https://doi.org/10.1016/S0096-3003(03)00738-0
  23. A. Golbabai, M. Javidi, A spectral domain decomposition approach for the generalized Burger's-Fisher equation, Chaos Solitons and Fractals, vol. 39, no. 1, pp. 385392, 2009. https://doi.org/10.1016/j.chaos.2007.04.013
  24. N. Bildik, A. Konuralp, F. Bek, ,S. Kucukarslan, Solution of differentent type of the partial differential equation by differential transform method and Adomian's decomposition method, Appl. Math. Comput., vol. 7, pp. 551-567, 2006.
  25. X.Y. Wang, Exact and explicit solitary wave solutions for the generalized Fisher's equation, Phys. Lett. A, vol. 131, no.(4/5), pp. 277-279, 1988. https://doi.org/10.1016/0375-9601(88)90027-8