Solving Porous Medium Equation Using Aboodh Transform Homotopy Perturbation Method

Khalid Suliman Aboodh

doi:doi:10.11648/j.ajam.20160406.12

| Peer-Reviewed

Solving Porous Medium Equation Using Aboodh Transform Homotopy Perturbation Method

Khalid Suliman Aboodh

Published in American Journal of Applied Mathematics (Volume 4, Issue 6)

Received: 18 September 2016 Accepted: 10 October 2016 Published: 1 November 2016

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

In this paper, a new technique has been used forsolving the porous medium equation. This method is named by Aboodh transform which is a combination of the new integral transform “Aboodh transform” and the homotopy perturbation method. The nonlinear termin the porous medium equationscan be easily handled by homotopy perturbation method and some cases of these Equations are solved as examples to illustrate ability and reliability of mixture of Aboodh transform and homotopy perturbation method. The results reveal that the combination of Aboodh transform and homotopy perturbation methodis quite capable, practically well appropriate for usingsuch theproblems. Also, this method is found that a better alternative method to some existing techniques for such realistic problems.

Published in	American Journal of Applied Mathematics (Volume 4, Issue 6)
DOI	10.11648/j.ajam.20160406.12
Page(s)	271-276
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, Non Linear Partial Differential Equation, Porous Medium Equation

References

[1]	A. D. Polyanin, V. F. Zaitsev (2004), Handbook of Nonlinear Partial Differential Equations, Chapman and Hall/CRC Press, Boca Raton,2004.
[2]	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, pp2041-2046.
[3]	Juan Luis Vazquez (2007), The Porous Medium Equation Mathematical Theory, Oxford Science Publication, Clarenden Press, pp1-28.
[4]	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 Approximationand Applications ISSN: 2326-9790 (Print);February 2016.
[5]	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.
[6]	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.
[7]	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.
[8]	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
[9]	Tarig M. ElzakiandSalih M. Elzaki, Applications of New Trans form “ELzaki Transform” to Partial Differential Equations, Global Journal of Pure and Applied Mathematics, (7)1, 2011, pp 65-70.
[10]	He J. Homotopy-perturbation method for solving boundary value problem, Phys Lett A, 350 (2006), 87-88.
[11]	Prem Kiran and G. Bhadane, ELzaki Transform Homotopy-perturbation method for solving Porous equation, International Journal of Research in Engineering and Technology,Volume: 02 Issue: 12- Dec-2013.
[12]	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.
[13]	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, pp33-42.

Cite This Article

Plain Text BibTeX RIS

APA Style

Khalid Suliman Aboodh. (2016). Solving Porous Medium Equation Using Aboodh Transform Homotopy Perturbation Method. American Journal of Applied Mathematics, 4(6), 271-276. https://doi.org/10.11648/j.ajam.20160406.12

Copy | Download

ACS Style

Khalid Suliman Aboodh. Solving Porous Medium Equation Using Aboodh Transform Homotopy Perturbation Method. Am. J. Appl. Math. 2016, 4(6), 271-276. doi: 10.11648/j.ajam.20160406.12

Copy | Download

AMA Style

Khalid Suliman Aboodh. Solving Porous Medium Equation Using Aboodh Transform Homotopy Perturbation Method. Am J Appl Math. 2016;4(6):271-276. doi: 10.11648/j.ajam.20160406.12

Copy | Download

@article{10.11648/j.ajam.20160406.12,
  author = {Khalid Suliman Aboodh},
  title = {Solving Porous Medium Equation Using Aboodh Transform Homotopy Perturbation Method},
  journal = {American Journal of Applied Mathematics},
  volume = {4},
  number = {6},
  pages = {271-276},
  doi = {10.11648/j.ajam.20160406.12},
  url = {https://doi.org/10.11648/j.ajam.20160406.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20160406.12},
  abstract = {In this paper, a new technique has been used forsolving the porous medium equation. This method is named by Aboodh transform which is a combination of the new integral transform “Aboodh transform” and the homotopy perturbation method. The nonlinear termin the porous medium equationscan be easily handled by homotopy perturbation method and some cases of these Equations are solved as examples to illustrate ability and reliability of mixture of Aboodh transform and homotopy perturbation method. The results reveal that the combination of Aboodh transform and homotopy perturbation methodis quite capable, practically well appropriate for usingsuch theproblems. Also, this method is found that a better alternative method to some existing techniques for such realistic problems.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Solving Porous Medium Equation Using Aboodh Transform Homotopy Perturbation Method
AU  - Khalid Suliman Aboodh
Y1  - 2016/11/01
PY  - 2016
N1  - https://doi.org/10.11648/j.ajam.20160406.12
DO  - 10.11648/j.ajam.20160406.12
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 271
EP  - 276
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20160406.12
AB  - In this paper, a new technique has been used forsolving the porous medium equation. This method is named by Aboodh transform which is a combination of the new integral transform “Aboodh transform” and the homotopy perturbation method. The nonlinear termin the porous medium equationscan be easily handled by homotopy perturbation method and some cases of these Equations are solved as examples to illustrate ability and reliability of mixture of Aboodh transform and homotopy perturbation method. The results reveal that the combination of Aboodh transform and homotopy perturbation methodis quite capable, practically well appropriate for usingsuch theproblems. Also, this method is found that a better alternative method to some existing techniques for such realistic problems.
VL  - 4
IS  - 6
ER  -

Copy | Download

Author Information

Khalid Suliman Aboodh

Department of Mathematics, Faculty of Science &Technology, Omdurman Islamic University, Khartoum, Sudan

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Khalid Suliman Aboodh. (2016). Solving Porous Medium Equation Using Aboodh Transform Homotopy Perturbation Method. American Journal of Applied Mathematics, 4(6), 271-276. https://doi.org/10.11648/j.ajam.20160406.12

Copy | Download

ACS Style

Khalid Suliman Aboodh. Solving Porous Medium Equation Using Aboodh Transform Homotopy Perturbation Method. Am. J. Appl. Math. 2016, 4(6), 271-276. doi: 10.11648/j.ajam.20160406.12

Copy | Download

AMA Style

Khalid Suliman Aboodh. Solving Porous Medium Equation Using Aboodh Transform Homotopy Perturbation Method. Am J Appl Math. 2016;4(6):271-276. doi: 10.11648/j.ajam.20160406.12

Copy | Download

@article{10.11648/j.ajam.20160406.12,
  author = {Khalid Suliman Aboodh},
  title = {Solving Porous Medium Equation Using Aboodh Transform Homotopy Perturbation Method},
  journal = {American Journal of Applied Mathematics},
  volume = {4},
  number = {6},
  pages = {271-276},
  doi = {10.11648/j.ajam.20160406.12},
  url = {https://doi.org/10.11648/j.ajam.20160406.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20160406.12},
  abstract = {In this paper, a new technique has been used forsolving the porous medium equation. This method is named by Aboodh transform which is a combination of the new integral transform “Aboodh transform” and the homotopy perturbation method. The nonlinear termin the porous medium equationscan be easily handled by homotopy perturbation method and some cases of these Equations are solved as examples to illustrate ability and reliability of mixture of Aboodh transform and homotopy perturbation method. The results reveal that the combination of Aboodh transform and homotopy perturbation methodis quite capable, practically well appropriate for usingsuch theproblems. Also, this method is found that a better alternative method to some existing techniques for such realistic problems.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Solving Porous Medium Equation Using Aboodh Transform Homotopy Perturbation Method
AU  - Khalid Suliman Aboodh
Y1  - 2016/11/01
PY  - 2016
N1  - https://doi.org/10.11648/j.ajam.20160406.12
DO  - 10.11648/j.ajam.20160406.12
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 271
EP  - 276
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20160406.12
AB  - In this paper, a new technique has been used forsolving the porous medium equation. This method is named by Aboodh transform which is a combination of the new integral transform “Aboodh transform” and the homotopy perturbation method. The nonlinear termin the porous medium equationscan be easily handled by homotopy perturbation method and some cases of these Equations are solved as examples to illustrate ability and reliability of mixture of Aboodh transform and homotopy perturbation method. The results reveal that the combination of Aboodh transform and homotopy perturbation methodis quite capable, practically well appropriate for usingsuch theproblems. Also, this method is found that a better alternative method to some existing techniques for such realistic problems.
VL  - 4
IS  - 6
ER  -

Copy | Download