APPROXIMATE SOLUTION FOR BURGER'S-FISHER EQUATION BY VARIATIONAL ITERATION TRANSFORM METHOD
Article Sidebar
Main Article Content
Abstract
Nonlinear partial differential equations represent the most important phenomena occurring in the world and are encountered in various fields of science. Generalized Burger’s-Fisher equation is very important for describing different mechanisms. Burger’s-Fisher equation arises in the field of applied mathematics and physics applications. This equation shows a prototypical model for describing the interaction between the reaction mechanisms, convection effect, and diffusion transport. In this paper, variational iteration transform method that combines Laplace transform and the variational iteration method, which used to obtain approximate analytical solutions of Burger’s - Fisher equation. Comparison of the results obtained by the present method with the exact solution and other existing methods reveals the accuracy and fast convergence of the proposed method.
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
Tikrit Journal of Pure Science is licensed under the Creative Commons Attribution 4.0 International License, which allows users to copy, create extracts, abstracts, and new works from the article, alter and revise the article, and make commercial use of the article (including reuse and/or resale of the article by commercial entities), provided the user gives appropriate credit (with a link to the formal publication through the relevant DOI), provides a link to the license, indicates if changes were made, and the licensor is not represented as endorsing the use made of the work. The authors hold the copyright for their published work on the Tikrit J. Pure Sci. website, while Tikrit J. Pure Sci. is responsible for appreciate citation of their work, which is released under CC-BY-4.0, enabling the unrestricted use, distribution, and reproduction of an article in any medium, provided that the original work is properly cited.
References
[1] Wang, X.Y. (1988). Exact and explicit solitary wave solutions for the generalized Fisher equation. Phys Lett A, 131(4/5):277–9.
[2] Jeffrey, A. and Mohamad, M.N.B. (1991). Exact solutions to the KdV–Burgers equation. Wave Motion, 14:369–75.
[3] Wadati, M. (1972). The exact solution of the modified Korteweg–de Vries equation. J Phys Soc Jpn , 32:1681–7.
[4] Kivshar, Y.S, and Pelinovsky, D.E. (2000). Self-focusing and transverse instabilities of solitary waves. Phys Rep, 331:117–95.
[5] Hereman, W. and Takaoka, M. (1990). Solitary wave solutions of nonlinear evolution and wave equations using a direct method and MACSYMA. J Phys A ;23:4805–22. [6] Javidi, M. (1990). A numerical solution of the generalized Burger’s–Huxley equation by pseudospectral method and Darvishi’s preconditioning. Appl Math Comput , 175:1619–28. [7] Javidi, M. (2006). A numerical solution of the generalized Burger’s–Huxley equation by spectral collocation method. Appl Math Comput , 178(2) :338–44.
[8] Adomian, G. (1994). Solving frontier problems of physics: the decomposition method. Boston: Kluwer Academic.
[9] Hashim; I. Noorani, M.S.M. and Batiha, B. (2006). A note on the Adomian decomposition method for the generalized Huxley equation. Appl Math Comput, doi:10.1016/16.amc .03.011, in press.
[10] Hashim; I. Noorani, M.S.M. and Al-Hadidi, M.R.S. (2006). Solving the generalized Burgers–Huxley equation using the Adomian decomposition method. Math Comput Model, 43:1404–11.
[11] He, JH. (2005). Application of homotopy perturbation method to nonlinear wave equations. Chaos, Solitons & Fractals , 26(3) : 695–700.
[12] He, JH. (2005). Homotopy perturbation method for bifurcation of nonlinear problems. Int J Nonlin Sci Numer Simul, 6(2):207–8.
[13] He, J.H. (2005). Limit cycle and bifurcation of nonlinear problems. Chaos, Solitons & Fractals, 26(3):827–33.
[14] He, J.H. (1997). A new approach to nonlinear partial differential equations. Communications in nonlinear Science and Numerical Simulation, 2(4):230–235.
[15] He, J.H. (1997). Variational iteration method for delay differential equations. Communications in nonlinear Science and Numerical Simulation, 2(4):235–6.
[16] He, J.H. (1999). Variational iteration method – a kind of non-linear analytical technique: some examples International Journal of Non-Linear Mechanics, 34(4):699–708.
[17] He, J.H. (2000). Variational iteration method for autonomous ordinary differential systems. Applied Mathematics and Computation, 114(2–3):115–23.
[18] He, J.H. (2003). A simple perturbation approach to Blasius equation.Applied Mathematics and Computation, 140(2–3):217–22.
[19] He; J.H. Wan, Y-Q. and Guo, Q. (2004). An iteration formulation for normalized diode characteristics. International Journal of Circut Theory and Application, 32(6):629–32.
[20] Abdou, M.A. and Soliman, A.A. (2005). Variational iteration method for solving Burger’s and coupled Burger’s equations. Journal of Computional and Application Mathematics ,181(2):245–251.
[21] Momani, S. and Abuasad, S. (2006). Application of He’s variational iteration method to Helmholtz equation. Chaos, Solitons & Fractals, 27(5):1119–23.
[22] Moghimi, M. and Hejazi, F.S.A. (2007). Variational iteration method for solving generalized Burger–Fisher and Burger equations. Chaos, Solitons & Fractals, 33(5): 1756-1761.
[23] Satsuma, J. (1987). Topics in soliton theory and exactly solvable nonlinear equations. Singapore: World Scientific.
[24] Toheeb; A. Oladapo, O. and Yusuf, O. (2014). A Combination of the Laplace Transform and the Variational Iteration Method for the Analytical Treatment of Delay Differential Equations. International Journal of Differential Equations and Applications, 13 (3): 164-175.
[25] Kocacoban; D., Koc, A. B. Kurnaz, A. and Keskin, Y. (2011). A Better Approximation to the Solution of Burger-Fisher Equation. Proceedings of the World Congress on Engineering Vol I, WCE 2011, July 6 - 8, 2011, London, U.K.