Application of diff erential transformation method to the fi sher equation.
محورهای موضوعی : Applied Mathematics
B. Soltanalizadeh
1
(Young Researchers Club, Sarab Branch, Islamic Azad University, Sarab,
Iran.)
B. Babayar
2
(Department of Mathematics, Islamic Azad University, Sarab Branch, Sarab,
Iran.)
کلید واژه: Fisher equation, Di erential, Transformation method, Spectral method,
چکیده مقاله :
In this paper, the di erential transform method (DTM) is applied to the Fisherequation. This method can be used to obtain the exact solutions of Fisherequation. Finally, we give some examples to illustrate the suciency of themethod for solving such nonlinear partial di erential equations. These resultsshow that this technique is easy to apply.
In this paper, the di erential transform method (DTM) is applied to the Fisherequation. This method can be used to obtain the exact solutions of Fisherequation. Finally, we give some examples to illustrate the suciency of themethod for solving such nonlinear partial di erential equations. These resultsshow that this technique is easy to apply.
[1] R. Abazari, A. Borhanifar, Numerical study of the solution of the Burgers
and coupled Burgers equations by a di erential transformation method,
Comput. Math. Appl., 59 (2010) 2711{2722.
[2] D. Agirseven, T. Ozis, An analytical study for Fisher type equations by
using homotopy perturbation method, Computers Math. with Appl., 60
(2010) 602{609
[3] K. Al-Khaled, Numerical study of Fishers reactiondi usion equation by
the Sinc collocation method, J. Comput. Appl. Math. 137 (2001) 245-255.
[4] F. Ayaz, Solutions of the systems of di erential equations by di erential
transform method, Appl. Math. Comput., 147 (2004) 547-567.
[5] A. Borhanifar, R. Abazari, Numerical study of nonlinear Schrodinger and
coupled Schrodinger equations by di erential transformation method, Opt.
Commu. 283 (2010) 2026{2031.
[6] J.P. Boyd, Chebyshev and Fourier Spectral Methods, Dover, New York,
2000.
[7] C.K. Chen, S.H. Ho, Solving partial di erential equations by two
dimensional di erential transform method, Appl. Math. Comput., 106
(1999) 171{179.
[8] A. Gokdogoan, M. Merdan, A. Yildirim, A
multistage di erential transformation method for approximate solution
of Hantavirus infection model. Commun Nonlinear Sci Numer Simulat.,
(2011), doi:10.1016/j.cnsns.2011.05.023.
[9] G.F. Carey, Y. Shen, Least-squares nite element approximation of Fishers
reactiondi usion equation, Numer. Methods Part. Di er. Eq. 11 (1995)
175-186.
[10] H.R. Ghehsareh, B. Soltanalizadeh,S. Abbasbandy, A matrix formulation
to the wave equation with nonlocal boundary condition, Inter. J. Comput.
Math., 88 (2011) 1681{1696.
[11] S.A. Gourley, Travelling front solutions of a nolocal Fisher equation, J.
Math. Biol. 41 (2000) 272-284.
[12] G. Hariharan, K. Kannan, K.R. Sharma, Haar wavelet method for solving
Fishers equation, Appl. Math. Comput., 211 (2009) 284-292.
[13] J.K. Hunter and J. Scheurle, Existence of perturbed solitary wave
solutions to a model equation for water waves, Physica D, 32 (1988) 253.
[14] M.J. Jang, C.L. Chen, Analysis of the response of a strongly nonlinear
damped system using a di erential transformation technique , Appl. Math.
Comput. 88 (1997) 137{151.
[15] M. J. Jang, C. K. Chen, Two-dimensional di erential transformation
method for partial di erantial equations, Appl. Math. Copmut. 121 (2001)
261{270.
[16] M. Merdan, A. Gokdogan, A. Yildirim, Approximate analytical
solution for time-dependent Emden-Fowler type di erential equations by
di erential transformation method, World Applied Sciences Journal, in
press.
[17] S. Shahmorad, A. Borhanifar, B. Soltanalizadeh, A matrix formulation
of the heat equation with nonlocal boundary conditions, Comput. Met.
Appl. Math., in press.
[18] B. Soltanalizadeh, Numerical analysis of the one-dimensional Heat
equation subject to a boundary integral speci cation, Opt. Commu., 284
(2011) 2109-2112.
[19] B. Soltanalizadeh, M. Zarebnia, Numerical analysis of the linear
and nonlinear Kuramoto-Sivashinsky equation by using Di erential
Transformation method, Inter. J. Appl. Math. Mechanics, 7(12) (2011)
63{72.
[20] B. Soltanalizadeh, Di erential Transformation method for solving onespace-
dimensional Telegraph equation, comput. appl. math., in Press.
[21] B. Soltanalizadeh, Numerical analysis of Kawahara equation by the
Di erential Transformation method, Aust. J. Basic Appl. Sci., in press.
[22] B. Soltanalizadeh, Application of Di erential Transformation method for
solving a fourth-order parabolic partial di erential equations, Inter. j. pure
appl. math., in press.
[23] A.M. Wazwaz, A. Gorguis, An analytical study of Fisher's equation by
using Adomian decomposition method, Appl. Math. Comput., 154 (2004)
609-620.
[24] J.K. Zhou, Di erential Transformation and Its Applications for Electrical
Circuits, Huazhong University Press, Wuhan, China, 1986 (in Chinese).
