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

Mohannad H. Eljaily; Tarig M. Elzaki

doi:doi:10.11648/j.pamj.20150406.17

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

Mohannad H. Eljaily, Tarig M. Elzaki

Published in Pure and Applied Mathematics Journal (Volume 4, Issue 6)

Received: 12 October 2015 Accepted: 21 October 2015 Published: 3 November 2015

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Abstract

In this paper, a combined form of the Laplace transforms method with the homotopy perturbation method is proposed to solve Korteweg-DeVries (KDV) Equation. This method is called the homotopy perturbation transform method (HPTM). The (HPTM) finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. The results reveal that the proposed method is very efficient, simple and can be applied to other nonlinear problems.

Published in	Pure and Applied Mathematics Journal (Volume 4, Issue 6)
DOI	10.11648/j.pamj.20150406.17
Page(s)	264-268
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), 2024. Published by Science Publishing Group

Keywords

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

References

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APA Style

Mohannad H. Eljaily, Tarig M. Elzaki. (2015). Homotopy Perturbation Transform Method for Solving Korteweg-DeVries (KDV) Equation. Pure and Applied Mathematics Journal, 4(6), 264-268. https://doi.org/10.11648/j.pamj.20150406.17

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ACS Style

Mohannad H. Eljaily; Tarig M. Elzaki. Homotopy Perturbation Transform Method for Solving Korteweg-DeVries (KDV) Equation. Pure Appl. Math. J. 2015, 4(6), 264-268. doi: 10.11648/j.pamj.20150406.17

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AMA Style

Mohannad H. Eljaily, Tarig M. Elzaki. Homotopy Perturbation Transform Method for Solving Korteweg-DeVries (KDV) Equation. Pure Appl Math J. 2015;4(6):264-268. doi: 10.11648/j.pamj.20150406.17

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@article{10.11648/j.pamj.20150406.17,
  author = {Mohannad H. Eljaily and Tarig M. Elzaki},
  title = {Homotopy Perturbation Transform Method for Solving Korteweg-DeVries (KDV) Equation},
  journal = {Pure and Applied Mathematics Journal},
  volume = {4},
  number = {6},
  pages = {264-268},
  doi = {10.11648/j.pamj.20150406.17},
  url = {https://doi.org/10.11648/j.pamj.20150406.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20150406.17},
  abstract = {In this paper, a combined form of the Laplace transforms method with the homotopy perturbation method is proposed to solve Korteweg-DeVries (KDV) Equation. This method is called the homotopy perturbation transform method (HPTM). The (HPTM) finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. The results reveal that the proposed method is very efficient, simple and can be applied to other nonlinear problems.},
 year = {2015}
}

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TY  - JOUR
T1  - Homotopy Perturbation Transform Method for Solving Korteweg-DeVries (KDV) Equation
AU  - Mohannad H. Eljaily
AU  - Tarig M. Elzaki
Y1  - 2015/11/03
PY  - 2015
N1  - https://doi.org/10.11648/j.pamj.20150406.17
DO  - 10.11648/j.pamj.20150406.17
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 264
EP  - 268
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20150406.17
AB  - In this paper, a combined form of the Laplace transforms method with the homotopy perturbation method is proposed to solve Korteweg-DeVries (KDV) Equation. This method is called the homotopy perturbation transform method (HPTM). The (HPTM) finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. The results reveal that the proposed method is very efficient, simple and can be applied to other nonlinear problems.
VL  - 4
IS  - 6
ER  -

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Author Information

Mohannad H. Eljaily

Department of Mathematic, Faculty of Sciences, Sudan University of Sciences and Technology, Khartoum, Sudan
Tarig M. Elzaki

Mathematics Department, Faculty of Sciences and Arts-Alkamil, University of Jeddah, Jeddah, Saudi Arabia

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APA Style

Mohannad H. Eljaily, Tarig M. Elzaki. (2015). Homotopy Perturbation Transform Method for Solving Korteweg-DeVries (KDV) Equation. Pure and Applied Mathematics Journal, 4(6), 264-268. https://doi.org/10.11648/j.pamj.20150406.17

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ACS Style

Mohannad H. Eljaily; Tarig M. Elzaki. Homotopy Perturbation Transform Method for Solving Korteweg-DeVries (KDV) Equation. Pure Appl. Math. J. 2015, 4(6), 264-268. doi: 10.11648/j.pamj.20150406.17

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AMA Style

Mohannad H. Eljaily, Tarig M. Elzaki. Homotopy Perturbation Transform Method for Solving Korteweg-DeVries (KDV) Equation. Pure Appl Math J. 2015;4(6):264-268. doi: 10.11648/j.pamj.20150406.17

Copy | Download

@article{10.11648/j.pamj.20150406.17,
  author = {Mohannad H. Eljaily and Tarig M. Elzaki},
  title = {Homotopy Perturbation Transform Method for Solving Korteweg-DeVries (KDV) Equation},
  journal = {Pure and Applied Mathematics Journal},
  volume = {4},
  number = {6},
  pages = {264-268},
  doi = {10.11648/j.pamj.20150406.17},
  url = {https://doi.org/10.11648/j.pamj.20150406.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20150406.17},
  abstract = {In this paper, a combined form of the Laplace transforms method with the homotopy perturbation method is proposed to solve Korteweg-DeVries (KDV) Equation. This method is called the homotopy perturbation transform method (HPTM). The (HPTM) finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. The results reveal that the proposed method is very efficient, simple and can be applied to other nonlinear problems.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Homotopy Perturbation Transform Method for Solving Korteweg-DeVries (KDV) Equation
AU  - Mohannad H. Eljaily
AU  - Tarig M. Elzaki
Y1  - 2015/11/03
PY  - 2015
N1  - https://doi.org/10.11648/j.pamj.20150406.17
DO  - 10.11648/j.pamj.20150406.17
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 264
EP  - 268
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20150406.17
AB  - In this paper, a combined form of the Laplace transforms method with the homotopy perturbation method is proposed to solve Korteweg-DeVries (KDV) Equation. This method is called the homotopy perturbation transform method (HPTM). The (HPTM) finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. The results reveal that the proposed method is very efficient, simple and can be applied to other nonlinear problems.
VL  - 4
IS  - 6
ER  -

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