The Solution of Porous Medium Equation by Aboodh Homotopy Perturbation Method

Mohand M. Abdelrahim Mahgoub; Abdelilah K. Hassan Sedeeg

doi:doi:10.11648/j.ajam.20160405.13

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The Solution of Porous Medium Equation by Aboodh Homotopy Perturbation Method

Mohand M. Abdelrahim Mahgoub, Abdelilah K. Hassan Sedeeg

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

Received: 26 August 2016 Accepted: 3 September 2016 Published: 9 October 2016

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Abstract

In this paper, the homotopy perturbation method (HPM) and Aboodh transform are employed to obtain analytical solution of the porous medium equation. The proposed method (ATHPM) is an elegant combination of the new integral transform “Aboodh Transform” and the homotopy perturbation method. The porous medium equations have importance in engineering and sciences and constitute a good model for many systems in various fields. The results tell us that the proposed method is more efficient and easier to handle when is compared with existing other methods in such partial differential equations.

Published in	American Journal of Applied Mathematics (Volume 4, Issue 5)
DOI	10.11648/j.ajam.20160405.13
Page(s)	217-221
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

Aboodh Transform, Homotopy Perturbation Method, Non Linear Partial Differential Equation, Porous Medium Equation

References

[1]	K. S. Aboodh, The New Integral Transform “Aboodh Transform” Global Journal of pure and Applied Mathematics, 9 (1), 35-43 (2013).
[2]	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).
[3]	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.
[4]	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.
[5]	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.
[6]	Juan Luis Vazquez (2007), The Porous Medium Equation Mathematical Theory, Oxford Science Publication, Clarenden Press, pp 1-28.
[7]	Prem Kiran G. Bhadane1, V. H. Pradhan, Elzaki Transform Homotopy Perturbation Method For Solving Porous Medium Equation, international journal of research in ingineering and technology, pissn: 2321-7308.
[8]	Tarig M. Elzaki and Eman M. A. Hilal (2012), Homotopy Perturbation and ELzaki Transform for solving Nonlinear Partial Differential equations, Mathematical Theory and Modeling, Vol. 2,No. 3, pp 33-42.
[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, pp 65-70.
[10]	Tarig M. Elzaki (2011), The New Integral Transform “ELzaki Transform”, Global Journal of Pure and Applied Mathematics, Vol. 7, No. 1, pp 5764.
[11]	Biazar, J., Ghazvini, H., 2007. Exact solutions for nonlinear Schrodinger equations by He’s homotopy perturbation method. Physics Letter A 366, 79-84.

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APA Style

Mohand M. Abdelrahim Mahgoub, Abdelilah K. Hassan Sedeeg. (2016). The Solution of Porous Medium Equation by Aboodh Homotopy Perturbation Method. American Journal of Applied Mathematics, 4(5), 217-221. https://doi.org/10.11648/j.ajam.20160405.13

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ACS Style

Mohand M. Abdelrahim Mahgoub; Abdelilah K. Hassan Sedeeg. The Solution of Porous Medium Equation by Aboodh Homotopy Perturbation Method. Am. J. Appl. Math. 2016, 4(5), 217-221. doi: 10.11648/j.ajam.20160405.13

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AMA Style

Mohand M. Abdelrahim Mahgoub, Abdelilah K. Hassan Sedeeg. The Solution of Porous Medium Equation by Aboodh Homotopy Perturbation Method. Am J Appl Math. 2016;4(5):217-221. doi: 10.11648/j.ajam.20160405.13

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@article{10.11648/j.ajam.20160405.13,
  author = {Mohand M. Abdelrahim Mahgoub and Abdelilah K. Hassan Sedeeg},
  title = {The Solution of Porous Medium Equation by Aboodh Homotopy Perturbation Method},
  journal = {American Journal of Applied Mathematics},
  volume = {4},
  number = {5},
  pages = {217-221},
  doi = {10.11648/j.ajam.20160405.13},
  url = {https://doi.org/10.11648/j.ajam.20160405.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20160405.13},
  abstract = {In this paper, the homotopy perturbation method (HPM) and Aboodh transform are employed to obtain analytical solution of the porous medium equation. The proposed method (ATHPM) is an elegant combination of the new integral transform “Aboodh Transform” and the homotopy perturbation method. The porous medium equations have importance in engineering and sciences and constitute a good model for many systems in various fields. The results tell us that the proposed method is more efficient and easier to handle when is compared with existing other methods in such partial differential equations.},
 year = {2016}
}

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TY  - JOUR
T1  - The Solution of Porous Medium Equation by Aboodh Homotopy Perturbation Method
AU  - Mohand M. Abdelrahim Mahgoub
AU  - Abdelilah K. Hassan Sedeeg
Y1  - 2016/10/09
PY  - 2016
N1  - https://doi.org/10.11648/j.ajam.20160405.13
DO  - 10.11648/j.ajam.20160405.13
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 217
EP  - 221
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20160405.13
AB  - In this paper, the homotopy perturbation method (HPM) and Aboodh transform are employed to obtain analytical solution of the porous medium equation. The proposed method (ATHPM) is an elegant combination of the new integral transform “Aboodh Transform” and the homotopy perturbation method. The porous medium equations have importance in engineering and sciences and constitute a good model for many systems in various fields. The results tell us that the proposed method is more efficient and easier to handle when is compared with existing other methods in such partial differential equations.
VL  - 4
IS  - 5
ER  -

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Author Information

Mohand M. Abdelrahim Mahgoub

Mathematics Department Faculty of Sciences and Arts Almikwah, Albaha University, Albaha, Saudi Arabia; Mathematics Department Faculty of Sciences-Omdurman Islamic University, Khartoum, Sudan
Abdelilah K. 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

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APA Style

Mohand M. Abdelrahim Mahgoub, Abdelilah K. Hassan Sedeeg. (2016). The Solution of Porous Medium Equation by Aboodh Homotopy Perturbation Method. American Journal of Applied Mathematics, 4(5), 217-221. https://doi.org/10.11648/j.ajam.20160405.13

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ACS Style

Mohand M. Abdelrahim Mahgoub; Abdelilah K. Hassan Sedeeg. The Solution of Porous Medium Equation by Aboodh Homotopy Perturbation Method. Am. J. Appl. Math. 2016, 4(5), 217-221. doi: 10.11648/j.ajam.20160405.13

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AMA Style

Mohand M. Abdelrahim Mahgoub, Abdelilah K. Hassan Sedeeg. The Solution of Porous Medium Equation by Aboodh Homotopy Perturbation Method. Am J Appl Math. 2016;4(5):217-221. doi: 10.11648/j.ajam.20160405.13

Copy | Download

@article{10.11648/j.ajam.20160405.13,
  author = {Mohand M. Abdelrahim Mahgoub and Abdelilah K. Hassan Sedeeg},
  title = {The Solution of Porous Medium Equation by Aboodh Homotopy Perturbation Method},
  journal = {American Journal of Applied Mathematics},
  volume = {4},
  number = {5},
  pages = {217-221},
  doi = {10.11648/j.ajam.20160405.13},
  url = {https://doi.org/10.11648/j.ajam.20160405.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20160405.13},
  abstract = {In this paper, the homotopy perturbation method (HPM) and Aboodh transform are employed to obtain analytical solution of the porous medium equation. The proposed method (ATHPM) is an elegant combination of the new integral transform “Aboodh Transform” and the homotopy perturbation method. The porous medium equations have importance in engineering and sciences and constitute a good model for many systems in various fields. The results tell us that the proposed method is more efficient and easier to handle when is compared with existing other methods in such partial differential equations.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - The Solution of Porous Medium Equation by Aboodh Homotopy Perturbation Method
AU  - Mohand M. Abdelrahim Mahgoub
AU  - Abdelilah K. Hassan Sedeeg
Y1  - 2016/10/09
PY  - 2016
N1  - https://doi.org/10.11648/j.ajam.20160405.13
DO  - 10.11648/j.ajam.20160405.13
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 217
EP  - 221
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20160405.13
AB  - In this paper, the homotopy perturbation method (HPM) and Aboodh transform are employed to obtain analytical solution of the porous medium equation. The proposed method (ATHPM) is an elegant combination of the new integral transform “Aboodh Transform” and the homotopy perturbation method. The porous medium equations have importance in engineering and sciences and constitute a good model for many systems in various fields. The results tell us that the proposed method is more efficient and easier to handle when is compared with existing other methods in such partial differential equations.
VL  - 4
IS  - 5
ER  -

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