Aboodh Transform Homotopy Perturbation Method for Solving Third Order Korteweg -DeVries Equation

Khalid Suliman Aboodh

doi:doi:10.11648/j.ijtam.20160202.12

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Aboodh Transform Homotopy Perturbation Method for Solving Third Order Korteweg -DeVries Equation

Khalid Suliman Aboodh

Published in International Journal of Theoretical and Applied Mathematics (Volume 2, Issue 2)

Received: 18 September 2016 Accepted: 21 November 2016 Published: 22 November 2016

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Abstract

This Paper is discussing the theoretical approach of Aboodh transform [1] coupled with Homotopy Perturbation Method [3] that can be applied to higher order partial differential equations for finding exact as well as approximate solutions of the equations. Here Homotopy Perturbation Method using Aboodh transform [1], [16] has been applied to Korteweg-de vries equation which is of third order homogenous partial differential equation.

Published in	International Journal of Theoretical and Applied Mathematics (Volume 2, Issue 2)
DOI	10.11648/j.ijtam.20160202.12
Page(s)	35-39
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

Homotopy Perturbation, Korteweg-DeVries Equation, Aboodh Transforms

References

[1]	Khalid Suliman Aboodh, The New Integral Transform ''Aboodh Transform'' Global Journal of Pure and Applied Mathematics ISSN0973-1768 Volume 9, Number 1 (2013), pp. 35-43.
[2]	Elzaki, Tarig M & Eman M. A. (2012), Homotopy Perturbation and Elzaki Transform for Solving Nonlinear Partial Differential Equations, Mathematical Theory and Modeling, ISSN 2224-5804 Vol. 2.
[3]	Hemeda A. A (2012). Homotopy Perturbation Method for Solving Systems of Nonlinear Coupled Equations. Applied Mathematical Sciences, Vol. 6.
[4]	The Korteweg-de Vries Equation: History, exact Solutions, and graphical Representation by Klaus Brauer, University of Osnabrück/Germany, May 2000.
[5]	The Korteweg–de Vries equation: Its place in the development of nonlinear physics Peter S. Riseborough, Department of Physics, Temple University, Philadelphia, PA 19122, USA. for Solving Nonlinear Partial Differential Equations, Mathematical Theory and Modeling, ISSN 2224-5804 Vol. 2.
[6]	A. D. Polyanin, V. F. Zaitsev (2004), Handbook of Nonlinear Partial Differential Equations, Chapman and Hall/CRC Press, Boca Raton,. 2004.
[7]	Mishra D, Pradhan V. H., Mehta M. N. (2012), Solution of Porous Medium Equation by Homotopy Perturbation Transform Method, International Journal of Engineering Research and Applications, Vol. 2 Issue 3, pp 2041-2046.
[8]	Juan Luis Vazquez (2007), The Porous Medium Equation Mathematical Theory, Oxford Science Publication, Clarenden Press, pp1-28.
[9]	Tarig M. Elzaki and Salih M. Elzaki (2011), Applications of New Transform “ELzaki Transform” to Partial Differential Equations, Global Journal of Pure and Applied Mathematics, Vol. 7, No. 1, pp65-70.
[10]	Tarig M. Elzaki, Salih M. Elzaki and Elsayed A. Elnour(2012), On the New Integral Transform “ELzaki Transform” Fundamental Properties Investigations and Applications, Global Journal of Mathematical Sciences: Theory and Practical, Vol. 4, No. 1, pp1-13.
[11]	Khalid Suliman Aboodh, Application of New Transform "Aboodh Transform" to Partial Differential Equations ''Global Journal of Pure and Applied Mathematics ISSN 0973-1768 Volume 10, Number 2 (2014), pp. 249-254.
[12]	Tarig M. Elzaki andSalih M. Elzaki, Applications of New Transform “ELzaki Transform” to Partial Differential Equations, Global Journal of Pure and Applied Mathematics, (7)1, 2011, pp 65-70.
[13]	He J. Homotopy-perturbation method for solving boundary value problem, PhysLett A, 350 (2006), 87-88.
[14]	Shraddha S Chavan and Mihir M Panchal , Solution of Third Order Korteweg -De Vries Equation by Homotopy Perturbation Method Using Elzaki Transform, international Journal for research in applied science and engineering technology , Vol. 2 Issue VII, July 2014, pp 366-369.
[15]	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.
[16]	Khalid Suliman Aboodh, Homotopy Perturbation Method and Aboodh Transform for Solving Nonlinear Partial Differential Equations, Aboodh Transform for Solving Nonlinear Partial Differential Equations, Theory of Approximation and Applications ISSN: 2326-9790 (Print); February 2016.
[17]	Bellman R. perturbation Techniques in Mathematics, Physics and Engineering, Holt, Rinehart and Winston, New York, 1964.
[18]	O’Malley, Introduction to singular perturbation, Academic, New York, 1974.
[19]	Nayfeh AH. perturbation Methods, Wiley, New York, 1973.
[20]	Van Dyke M. Perturbation Methods in Fluid Mechanics, Annoted Edition, parabolic press, Stanford, CA, 1975.

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Khalid Suliman Aboodh. (2016). Aboodh Transform Homotopy Perturbation Method for Solving Third Order Korteweg -DeVries Equation. International Journal of Theoretical and Applied Mathematics, 2(2), 35-39. https://doi.org/10.11648/j.ijtam.20160202.12

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ACS Style

Khalid Suliman Aboodh. Aboodh Transform Homotopy Perturbation Method for Solving Third Order Korteweg -DeVries Equation. Int. J. Theor. Appl. Math. 2016, 2(2), 35-39. doi: 10.11648/j.ijtam.20160202.12

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AMA Style

Khalid Suliman Aboodh. Aboodh Transform Homotopy Perturbation Method for Solving Third Order Korteweg -DeVries Equation. Int J Theor Appl Math. 2016;2(2):35-39. doi: 10.11648/j.ijtam.20160202.12

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@article{10.11648/j.ijtam.20160202.12,
  author = {Khalid Suliman Aboodh},
  title = {Aboodh Transform Homotopy Perturbation Method for Solving Third Order Korteweg -DeVries Equation},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {2},
  number = {2},
  pages = {35-39},
  doi = {10.11648/j.ijtam.20160202.12},
  url = {https://doi.org/10.11648/j.ijtam.20160202.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20160202.12},
  abstract = {This Paper is discussing the theoretical approach of Aboodh transform [1] coupled with Homotopy Perturbation Method [3] that can be applied to higher order partial differential equations for finding exact as well as approximate solutions of the equations. Here Homotopy Perturbation Method using Aboodh transform [1], [16] has been applied to Korteweg-de vries equation which is of third order homogenous partial differential equation.},
 year = {2016}
}

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TY  - JOUR
T1  - Aboodh Transform Homotopy Perturbation Method for Solving Third Order Korteweg -DeVries Equation
AU  - Khalid Suliman Aboodh
Y1  - 2016/11/22
PY  - 2016
N1  - https://doi.org/10.11648/j.ijtam.20160202.12
DO  - 10.11648/j.ijtam.20160202.12
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 35
EP  - 39
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20160202.12
AB  - This Paper is discussing the theoretical approach of Aboodh transform [1] coupled with Homotopy Perturbation Method [3] that can be applied to higher order partial differential equations for finding exact as well as approximate solutions of the equations. Here Homotopy Perturbation Method using Aboodh transform [1], [16] has been applied to Korteweg-de vries equation which is of third order homogenous partial differential equation.
VL  - 2
IS  - 2
ER  -

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Author Information

Khalid Suliman Aboodh

Department of Mathematics, Faculty of Science &Technology, Omdurman Islamic University, Khartoum, Sudan;Department of Mathematics, Faculty of Science & Arts, University of Bisha, Bisha, KSA

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APA Style

Khalid Suliman Aboodh. (2016). Aboodh Transform Homotopy Perturbation Method for Solving Third Order Korteweg -DeVries Equation. International Journal of Theoretical and Applied Mathematics, 2(2), 35-39. https://doi.org/10.11648/j.ijtam.20160202.12

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ACS Style

Khalid Suliman Aboodh. Aboodh Transform Homotopy Perturbation Method for Solving Third Order Korteweg -DeVries Equation. Int. J. Theor. Appl. Math. 2016, 2(2), 35-39. doi: 10.11648/j.ijtam.20160202.12

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AMA Style

Khalid Suliman Aboodh. Aboodh Transform Homotopy Perturbation Method for Solving Third Order Korteweg -DeVries Equation. Int J Theor Appl Math. 2016;2(2):35-39. doi: 10.11648/j.ijtam.20160202.12

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@article{10.11648/j.ijtam.20160202.12,
  author = {Khalid Suliman Aboodh},
  title = {Aboodh Transform Homotopy Perturbation Method for Solving Third Order Korteweg -DeVries Equation},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {2},
  number = {2},
  pages = {35-39},
  doi = {10.11648/j.ijtam.20160202.12},
  url = {https://doi.org/10.11648/j.ijtam.20160202.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20160202.12},
  abstract = {This Paper is discussing the theoretical approach of Aboodh transform [1] coupled with Homotopy Perturbation Method [3] that can be applied to higher order partial differential equations for finding exact as well as approximate solutions of the equations. Here Homotopy Perturbation Method using Aboodh transform [1], [16] has been applied to Korteweg-de vries equation which is of third order homogenous partial differential equation.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Aboodh Transform Homotopy Perturbation Method for Solving Third Order Korteweg -DeVries Equation
AU  - Khalid Suliman Aboodh
Y1  - 2016/11/22
PY  - 2016
N1  - https://doi.org/10.11648/j.ijtam.20160202.12
DO  - 10.11648/j.ijtam.20160202.12
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 35
EP  - 39
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20160202.12
AB  - This Paper is discussing the theoretical approach of Aboodh transform [1] coupled with Homotopy Perturbation Method [3] that can be applied to higher order partial differential equations for finding exact as well as approximate solutions of the equations. Here Homotopy Perturbation Method using Aboodh transform [1], [16] has been applied to Korteweg-de vries equation which is of third order homogenous partial differential equation.
VL  - 2
IS  - 2
ER  -

Copy | Download