Solving Fourth Order Parabolic PDE with Variable Coefficients Using Aboodh Transform Homotopy Perturbation Method

Khalid Suliman Aboodh

doi:doi:10.11648/j.pamj.20150405.13

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Solving Fourth Order Parabolic PDE with Variable Coefficients Using Aboodh Transform Homotopy Perturbation Method

Khalid Suliman Aboodh

Published in Pure and Applied Mathematics Journal (Volume 4, Issue 5)

Received: 8 June 2015 Accepted: 15 June 2015 Published: 8 September 2015

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Abstract

Here, a new method called Aboodh transform homotopy perturbation method (ATHPM) is used to solve one dimensional fourth order parabolic linear partial differential equations with variable coefficients. The proposed method is a combination of the new integral transform “Aboodh transform” and the homotopy perturbation method. Some cases of one dimensional fourth order parabolic linear partial differential equations are solved to illustrate ability and reliability of mixture of Aboodh transform and homotopy perturbation method. We have compared the obtained analytical solution with the available Aboodh decomposition solution and homotopy perturbation method solution which is found to be exactly same. The results obtained reveal that the combination of Aboodh transform and homotopy perturbation method is quite capable, practically well appropriate for use in such problems.

Published in	Pure and Applied Mathematics Journal (Volume 4, Issue 5)
DOI	10.11648/j.pamj.20150405.13
Page(s)	219-224
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), 2015. Published by Science Publishing Group

Keywords

Aboodh Transform, Homotopy Perturbation Method, Linear Partial Differential Equation

References

[1]	Majid Khan, Muhammad Asif Gondal and Yasir Khan, An Efficient Laplace Decomposition algorithm for Fourth order Parabolic Partial Differential Equations with variable coefficients, World Applied Sciences Journal 13 (12), 2011, pp2463-2466.
[2]	Tarig M. Elzaki and Eman M. A. Hilal, Homotopy Perturbation and ELzaki Transform for solving Nonlinear Partial Differential equations, Mathematical Theory and Modeling, 2(3),2012, pp33-42.
[3]	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.
[4]	Hradyesh Kumar Mishra and Atulya K Nagar, He-Laplace Method for Linear and Nonlinear Partial Differential Equations, Journal of Applied Mathematics, Vol.2012,Article ID 180315, 16 pages.
[5]	Mehdi Dehghan and Jalil Manafian, The Solution of the Variable Coefficients Fourth-Order Parabolic Partial Differential Equations by the Homotopy Perturbation Method,Verlag der Zeitschrift fur Naturforschung, Tu¨bingen, 64a, 2009, pp420-430.
[6]	M. Hussain and Majid Khan, Modified Laplace Decomposition Method, Journal of Applied Mathematical Sciences, 4(36), 2010, pp 1769-1783.
[7]	Najeeb Alam Khan, Asmat Ara, Muhammad Afzal and Azam Khan, Analytical Aspect of Fourth order Parabolic Partial differential Equations with variable coefficients, Mathematical and Computational Applications, 15(3), 2010, pp. 481-489.
[8]	Khalid Suliman Aboodh, The New Integral Transform ''AboodhTransform''GlobalJournalofPure and Applied Mathematics ISSN0973-1768 Volume 9, Number 1 (2013), pp. 35-43.
[9]	Tarig M. Elzaki and Salih M. Elzaki, Applications of New Transform “ELzaki Transform” to Partial Differential Equations,Global Journal of Pure and Applied Mathematics, (7)1,2011,pp65-70.
[10]	He J. Homotopy-perturbation method for solving boundary value problem, Phys Lett A, 350 (2006), 87-88.

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APA Style

Khalid Suliman Aboodh. (2015). Solving Fourth Order Parabolic PDE with Variable Coefficients Using Aboodh Transform Homotopy Perturbation Method. Pure and Applied Mathematics Journal, 4(5), 219-224. https://doi.org/10.11648/j.pamj.20150405.13

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ACS Style

Khalid Suliman Aboodh. Solving Fourth Order Parabolic PDE with Variable Coefficients Using Aboodh Transform Homotopy Perturbation Method. Pure Appl. Math. J. 2015, 4(5), 219-224. doi: 10.11648/j.pamj.20150405.13

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AMA Style

Khalid Suliman Aboodh. Solving Fourth Order Parabolic PDE with Variable Coefficients Using Aboodh Transform Homotopy Perturbation Method. Pure Appl Math J. 2015;4(5):219-224. doi: 10.11648/j.pamj.20150405.13

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@article{10.11648/j.pamj.20150405.13,
  author = {Khalid Suliman Aboodh},
  title = {Solving Fourth Order Parabolic PDE with Variable Coefficients Using Aboodh Transform Homotopy Perturbation Method},
  journal = {Pure and Applied Mathematics Journal},
  volume = {4},
  number = {5},
  pages = {219-224},
  doi = {10.11648/j.pamj.20150405.13},
  url = {https://doi.org/10.11648/j.pamj.20150405.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20150405.13},
  abstract = {Here, a new method called Aboodh transform homotopy perturbation method (ATHPM) is used to solve one dimensional fourth order parabolic linear partial differential equations with variable coefficients. The proposed method is a combination of the new integral transform “Aboodh transform” and the homotopy perturbation method. Some cases of one dimensional fourth order parabolic linear partial differential equations are solved to illustrate ability and reliability of mixture of Aboodh transform and homotopy perturbation method. We have compared the obtained analytical solution with the available Aboodh decomposition solution and homotopy perturbation method solution which is found to be exactly same. The results obtained reveal that the combination of Aboodh transform and homotopy perturbation method is quite capable, practically well appropriate for use in such problems.},
 year = {2015}
}

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TY  - JOUR
T1  - Solving Fourth Order Parabolic PDE with Variable Coefficients Using Aboodh Transform Homotopy Perturbation Method
AU  - Khalid Suliman Aboodh
Y1  - 2015/09/08
PY  - 2015
N1  - https://doi.org/10.11648/j.pamj.20150405.13
DO  - 10.11648/j.pamj.20150405.13
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 219
EP  - 224
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20150405.13
AB  - Here, a new method called Aboodh transform homotopy perturbation method (ATHPM) is used to solve one dimensional fourth order parabolic linear partial differential equations with variable coefficients. The proposed method is a combination of the new integral transform “Aboodh transform” and the homotopy perturbation method. Some cases of one dimensional fourth order parabolic linear partial differential equations are solved to illustrate ability and reliability of mixture of Aboodh transform and homotopy perturbation method. We have compared the obtained analytical solution with the available Aboodh decomposition solution and homotopy perturbation method solution which is found to be exactly same. The results obtained reveal that the combination of Aboodh transform and homotopy perturbation method is quite capable, practically well appropriate for use in such problems.
VL  - 4
IS  - 5
ER  -

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Author Information

Khalid Suliman Aboodh

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

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APA Style

Khalid Suliman Aboodh. (2015). Solving Fourth Order Parabolic PDE with Variable Coefficients Using Aboodh Transform Homotopy Perturbation Method. Pure and Applied Mathematics Journal, 4(5), 219-224. https://doi.org/10.11648/j.pamj.20150405.13

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ACS Style

Khalid Suliman Aboodh. Solving Fourth Order Parabolic PDE with Variable Coefficients Using Aboodh Transform Homotopy Perturbation Method. Pure Appl. Math. J. 2015, 4(5), 219-224. doi: 10.11648/j.pamj.20150405.13

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AMA Style

Khalid Suliman Aboodh. Solving Fourth Order Parabolic PDE with Variable Coefficients Using Aboodh Transform Homotopy Perturbation Method. Pure Appl Math J. 2015;4(5):219-224. doi: 10.11648/j.pamj.20150405.13

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@article{10.11648/j.pamj.20150405.13,
  author = {Khalid Suliman Aboodh},
  title = {Solving Fourth Order Parabolic PDE with Variable Coefficients Using Aboodh Transform Homotopy Perturbation Method},
  journal = {Pure and Applied Mathematics Journal},
  volume = {4},
  number = {5},
  pages = {219-224},
  doi = {10.11648/j.pamj.20150405.13},
  url = {https://doi.org/10.11648/j.pamj.20150405.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20150405.13},
  abstract = {Here, a new method called Aboodh transform homotopy perturbation method (ATHPM) is used to solve one dimensional fourth order parabolic linear partial differential equations with variable coefficients. The proposed method is a combination of the new integral transform “Aboodh transform” and the homotopy perturbation method. Some cases of one dimensional fourth order parabolic linear partial differential equations are solved to illustrate ability and reliability of mixture of Aboodh transform and homotopy perturbation method. We have compared the obtained analytical solution with the available Aboodh decomposition solution and homotopy perturbation method solution which is found to be exactly same. The results obtained reveal that the combination of Aboodh transform and homotopy perturbation method is quite capable, practically well appropriate for use in such problems.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Solving Fourth Order Parabolic PDE with Variable Coefficients Using Aboodh Transform Homotopy Perturbation Method
AU  - Khalid Suliman Aboodh
Y1  - 2015/09/08
PY  - 2015
N1  - https://doi.org/10.11648/j.pamj.20150405.13
DO  - 10.11648/j.pamj.20150405.13
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 219
EP  - 224
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20150405.13
AB  - Here, a new method called Aboodh transform homotopy perturbation method (ATHPM) is used to solve one dimensional fourth order parabolic linear partial differential equations with variable coefficients. The proposed method is a combination of the new integral transform “Aboodh transform” and the homotopy perturbation method. Some cases of one dimensional fourth order parabolic linear partial differential equations are solved to illustrate ability and reliability of mixture of Aboodh transform and homotopy perturbation method. We have compared the obtained analytical solution with the available Aboodh decomposition solution and homotopy perturbation method solution which is found to be exactly same. The results obtained reveal that the combination of Aboodh transform and homotopy perturbation method is quite capable, practically well appropriate for use in such problems.
VL  - 4
IS  - 5
ER  -

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