Homotopy Perturbation Transform Method for Solving Third Order Korteweg-DeVries (KDV) Equation

Abdelilah Kamal Hassan Sedeeg

doi:doi:10.11648/j.ajam.20160405.16

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Homotopy Perturbation Transform Method for Solving Third Order Korteweg-DeVries (KDV) Equation

Abdelilah Kamal Hassan Sedeeg

Published in American Journal of Applied Mathematics (Volume 4, Issue 5)

Received: 4 September 2016 Accepted: 26 September 2016 Published: 18 October 2016

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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.

Published in	American Journal of Applied Mathematics (Volume 4, Issue 5)
DOI	10.11648/j.ajam.20160405.16
Page(s)	247-251
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Aboodh Transform, Homotopy Perturbation Method, Korteweg-DeVries (KDV) Equation

References

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[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.
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[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.
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[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).
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[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

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Abdelilah Kamal Hassan Sedeeg. (2016). Homotopy Perturbation Transform Method for Solving Third Order Korteweg-DeVries (KDV) Equation. American Journal of Applied Mathematics, 4(5), 247-251. https://doi.org/10.11648/j.ajam.20160405.16

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ACS Style

Abdelilah Kamal Hassan Sedeeg. Homotopy Perturbation Transform Method for Solving Third Order Korteweg-DeVries (KDV) Equation. Am. J. Appl. Math. 2016, 4(5), 247-251. doi: 10.11648/j.ajam.20160405.16

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AMA Style

Abdelilah Kamal Hassan Sedeeg. Homotopy Perturbation Transform Method for Solving Third Order Korteweg-DeVries (KDV) Equation. Am J Appl Math. 2016;4(5):247-251. doi: 10.11648/j.ajam.20160405.16

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@article{10.11648/j.ajam.20160405.16,
  author = {Abdelilah Kamal Hassan Sedeeg},
  title = {Homotopy Perturbation Transform Method for Solving Third Order Korteweg-DeVries (KDV) Equation},
  journal = {American Journal of Applied Mathematics},
  volume = {4},
  number = {5},
  pages = {247-251},
  doi = {10.11648/j.ajam.20160405.16},
  url = {https://doi.org/10.11648/j.ajam.20160405.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20160405.16},
  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.},
 year = {2016}
}

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TY  - JOUR
T1  - Homotopy Perturbation Transform Method for Solving Third Order Korteweg-DeVries (KDV) Equation
AU  - Abdelilah Kamal Hassan Sedeeg
Y1  - 2016/10/18
PY  - 2016
N1  - https://doi.org/10.11648/j.ajam.20160405.16
DO  - 10.11648/j.ajam.20160405.16
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 247
EP  - 251
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20160405.16
AB  - 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.
VL  - 4
IS  - 5
ER  -

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Author Information

Abdelilah Kamal Hassan Sedeeg

Mathematics Department Faculty of Sciences and Arts, Almikwah-Albaha University, Albaha, Saudi Arabia

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APA Style

Abdelilah Kamal Hassan Sedeeg. (2016). Homotopy Perturbation Transform Method for Solving Third Order Korteweg-DeVries (KDV) Equation. American Journal of Applied Mathematics, 4(5), 247-251. https://doi.org/10.11648/j.ajam.20160405.16

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ACS Style

Abdelilah Kamal Hassan Sedeeg. Homotopy Perturbation Transform Method for Solving Third Order Korteweg-DeVries (KDV) Equation. Am. J. Appl. Math. 2016, 4(5), 247-251. doi: 10.11648/j.ajam.20160405.16

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AMA Style

Abdelilah Kamal Hassan Sedeeg. Homotopy Perturbation Transform Method for Solving Third Order Korteweg-DeVries (KDV) Equation. Am J Appl Math. 2016;4(5):247-251. doi: 10.11648/j.ajam.20160405.16

Copy | Download

@article{10.11648/j.ajam.20160405.16,
  author = {Abdelilah Kamal Hassan Sedeeg},
  title = {Homotopy Perturbation Transform Method for Solving Third Order Korteweg-DeVries (KDV) Equation},
  journal = {American Journal of Applied Mathematics},
  volume = {4},
  number = {5},
  pages = {247-251},
  doi = {10.11648/j.ajam.20160405.16},
  url = {https://doi.org/10.11648/j.ajam.20160405.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20160405.16},
  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.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Homotopy Perturbation Transform Method for Solving Third Order Korteweg-DeVries (KDV) Equation
AU  - Abdelilah Kamal Hassan Sedeeg
Y1  - 2016/10/18
PY  - 2016
N1  - https://doi.org/10.11648/j.ajam.20160405.16
DO  - 10.11648/j.ajam.20160405.16
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 247
EP  - 251
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20160405.16
AB  - 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.
VL  - 4
IS  - 5
ER  -

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