Volume 4, Issue 5, October 2016, Page: 247-251
Homotopy Perturbation Transform Method for Solving Third Order Korteweg-DeVries (KDV) Equation
Abdelilah Kamal Hassan Sedeeg, Mathematics Department Faculty of Sciences and Arts, Almikwah-Albaha University, Albaha, Saudi Arabia; Mathematics Department Faculty of Education, Holy Quran and Islamic Sciences University, Khartoum, Sudan
Received: Sep. 4, 2016;       Accepted: Sep. 26, 2016;       Published: Oct. 18, 2016
DOI: 10.11648/j.ajam.20160405.16      View  2563      Downloads  117
Abstract
In this paper, we develop a method to calculate approximate solution of some Third-order Korteweg-de Vries equations with initial condition with the help of a new method called Aboodh transform homotopy perturbation method (ETHPM). This method is a combination of the new integral transform “Aboodh transform” and the homotopy perturbation method. The nonlinear term can be easily handled by homotopy perturbation method. The results reveal that the combination of Aboodh transform and homotopy perturbation method is quite capable, practically well appropriate for use in such problems and can be applied to other nonlinear problems. This method is seen as a better alternative method to some existing techniques for such realistic problems.
Keywords
Aboodh Transform, Homotopy Perturbation Method, Korteweg-DeVries (KDV) Equation
To cite this article
Abdelilah Kamal Hassan Sedeeg, Homotopy Perturbation Transform Method for Solving Third Order Korteweg-DeVries (KDV) Equation, American Journal of Applied Mathematics. Vol. 4, No. 5, 2016, pp. 247-251. doi: 10.11648/j.ajam.20160405.16
Copyright
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Reference
[1]
J. H. He, Homotopy perturbation technique, Computer Methods in Applied Mechanics and Engineering, 178 (1999):257-262.
[2]
N. H. Sweilam and M.M. Khader, Exact solutions of some coupled nonlinear partial differential equations using the homotopy perturbation method, Computers & Mathematics with Applications, 58 (2009):2134 2141.
[3]
A.M. Wazwas, A study on linear and non-linear Schrodinger equations by the variational iteration method, Chaos, Solitions and Fractals, 37 (4) (2008):1136 1142.
[4]
B. Jazbi and M. Moini, Application of He’s homotopy perturbation method for Schrodinger equation, Iranian Journalof Mathematical Sciences and Informatics, 3 (2) (2008):13-19.
[5]
J. H. He, Homotopy perturbation method: a new nonlinear analytical technique, Applied Mathematics and Computa- tion, 135 (2003):73-79.
[6]
J. H. He, Comparison of homotopy perturbation method and homotopy analysis method, Applied Mathematics and Computation, 156 (2004):527539.
[7]
Dogan Kaya, Mohammed Aassila, Application for a generalized KdV equation by the decomposition method, Physics Letters A 299 (2002) 201–206.
[8]
P. G. Drazin, R. S. Johnson, Solutions: An Introduction, Cambridge University Press, Cambridge, 1989.
[9]
P. Saucez, A. V. Wouwer, W. E. Schiesser, An adaptive method of lines solution of the Korteweg–de Vries equation, Computers & Mathematics with Applications 35 (12) (1998) 13–25.
[10]
T. A. Abassy, Magdy A. El-Tawil, H. El-Zoheiry, Exact solutions of some nonlinear partial differential equations using the variational iteration method linked with Laplace transforms and the Pad’e technique, Computers and Mathematics with Applications, doi:10.1016/j.camwa.2006.12.067.
[11]
F. Kangalgil, F. Ayaz, Solitary wave solutions for the KdV and KdV equations by differential transform method, Chaos, Solitons and Fractals, doi:10.1016/j.chaos.2008.02.009.
[12]
Mohannad H. Eljaily1, Tarig M. Elzaki, Homotopy Perturbation Transform Method for Solving Korteweg-DeVries (KDV) Equation, Pure and Applied Mathematics Journal 2015; 4 (6): 264-268.
[13]
K. S. Aboodh, The New Integral Transform “Aboodh Transform” Global Journal of pure and Applied Mathematics, 9 (1), 35-43 (2013).
[14]
K. S. Aboodh, Application of New Transform “Aboodh transform” to Partial Differential Equations, Global Journal of pure and Applied Math, 10 (2),249-254 (2014).
[15]
Khalid Suliman Aboodh, Homotopy Perturbation Method and Aboodh Transform for Solving Nonlinear Partial Differential Equations, Pure and Applied Mathematics Journal Volume 4, Issue 5, October 2015, Pages: 219-224.
[16]
Khalid Suliman Aboodh, Solving Fourth Order Parabolic PDE with Variable Coefficients Using Aboodh Transform Homotopy Perturbation Method, Pure and Applied Mathematics Journal 2015; 4 (5): 219-224.
[17]
L. Debnath, Nonlinear Partial Differential Equations for Scientists and Engineers, Birkhauser, Bostn, 1997.
[18]
J. D. Logan, An Introduction to Nonlinear Partial Differential Equations, Wiley, New York, 1994.
[19]
G. B. Whitham, Linear and Nonlinear Waves, Wiley, New York, 1974.
[20]
Sweilam, N. H. and M.M. Khader, 2009. Exact Solutions of some Capled nonlinear
Browse journals by subject