Homotopy Perturbation Method and Aboodh Transform for Solving Nonlinear Partial Differential Equations

Subject Areas : Applied Mathematics

Khalid Aboodh ¹

1 - Department of Mathematics Omdurman Islamic University (http: //www. fst. oiu. edu. sd) sudan

Received: 2015-03-12 Accepted : 2016-04-19 Published : 2017-05-01

Keywords: Homotopy Perturbation method, Aboodh transform, Nonlinear partial differential equations,

Abstract :

Here, a new method called Aboodh transform homotopy perturbation method(ATHPM) is used to solve nonlinear partial dierential equations, we presenta reliable combination of homotopy perturbation method and Aboodh transformto investigate some nonlinear partial dierential equations. The nonlinearterms can be handled by the use of homotopy perturbation method. The resultsshow the eciency of this method. Aboodh transform was introducedby Khalid Aboodh to facilitate the process of solving ordinary and partialdifferential equations in the time domain.

References:

[1]S. lslam, Yasir Khan, Naeem Faraz and Francis Austin (2010),
Numerical Solution of Logistic Dierential Equations by using the Laplace
Decomposition Method, World Applied Sciences Journal 8(9):1100-1105.
[2]Nuran Guzel and Muhammet Nurulay (2008), Solution of Shi Systems
By using Dierential Transform Method, Dunlupinar universities Fen
Bilimleri Enstitusu Dergisi, ISSN 1302-3055, PP. 49-59.
[3]Shin- Hsiang Chang , I-Ling Chang (2008), A new algorithm for
calculating one-dimensional dierential transform of nonlinear functions,
Applied Mathematics and Computation 195 ,799-808.
[4]Khalid Suliman Aboodh, The New Integral Transform Aboodh
Transform", GlobalJournal of Pure and Applied Mathematics ISSN 09731768
Volume 9, Number 1 (2013), pp. 35-43.
[5]Tarig M. Elzaki (2011), The New Integral Transform "Elzaki ransform?
Global Journal of Pure and Applied Mathematics, ISSN 09731768,Number
1, pp. 57-64.
[6]Tarig M. Elzaki and Salih M. Elzaki (2011), Application of New transform
?Elzaki Transform? to Partial Dierential Equations, Global Journal of
Pure and Applied Mathematics, ISSN 0973-1768,Number 1, pp.65-70.
[7]Tarig M. Elzaki and Salih M. Elzaki (2011), On the Connections between
Laplace and Elzaki transforms, Advances in Theoretical and Applied
Mathematics, ISSN 0973-4554 Volume 6, Number 1, pp. 1-11.
10
[8]Tarig M. Elzaki and Salih M. Elzaki (2011), On the Elzaki Transform and
Ordinary Dierential Equation With Variable Coecients, Advances in
Theoretical and Applied Mathematics. ISSN 0973-4554 Volume 6 Number
1, pp. 13-18.
[9]Lokenath Debnath and D. Bhatta (2006). Integral transform and their
Application second Edition,Chapman & Hall /CRC
[10]A.Kilicman and H.E.Gadain. (2009), An application of double Laplace
transform and Sumudu transform, Lobachevskii J. Math.30 (3) pp.214223.
[11]J. Zhang, (2007). A Sumudu based algorithm m for solving dierential
equations, Comp. Sci. J.Moldova 15(3), pp-303-313.
[12]Hassan Eltayeb and Adem kilicman, (2010), A Note on the Sumudu
Transforms and dierential Equations, Applied Mathematical Sciences,
VOL, 4, no.22,1089-1098
[13]Kilicman A.and H. ELtayeb. (2010), A note on Integral transform
and Partial Dierential Equation, Applied Mathematical Sciences,4(3),
PP.109-118.
[14]Hassan Eltayeh and Adem kilicman (2010), on Some Applications of a new
Integral Transform, Int.Journal of Math. Analysis, Vol, 4, no.3, 123-132.
[15]N.H. Sweilam, M.M. Khader (2009). Exact Solutions of some Capled
nonlinear partial dierential equations using the homotopy perturbation
method. Computers and Mathematics with Applications 58,2134-2141.
[16]P.R. Sharma and Giriraj Methi (2011). Applications of Homotopy
Perturbation method to Partial dierential equations. Asian Journal of
Mathematics and Statistics 4 (3): 140-150.
[17]M.A. Jafari, A. Aminataei (2010). Improved Homotopy Perturbation
Method. International Mathematical Forum, 5, no, 32, 1567-1579.
[18]Jagdev Singh, Devendra, Sushila. Homotopy Perturbation Sumudu
Transform Method for Nonlinear Equations. Adv. Theor. Appl. Mech.,
Vol. 4, 2011, no. 4, 165-175.
[19]Nuran Guzel and Muhammet Nurulay (2008), Solution of Shi Systems
By using Dierential Transform Method, Dunlupinar universities Fen
Bilimleri Enstitusu Dergisi, ISSN 1302-3055, PP. 49-59.
11
[20]Shin- Hsiang Chang , I-Ling Chang (2008), A new algorithm for
calculating one-dimensional dierential transform of nonlinear functions,
Applied Mathematics and Computation 195, 799-808.
[21]Hashim, I, Adomian decomposition method applied to the Lorenz system
chaos.08.135.
[22]Tarig M. Elzaki, Salih M. Elzaki, and Eman M. A. Hilal, (2012). Elzaki
and Sumudu Transforms for Solving Some Dierential Equations, Global
Journal of Pure and Applied Mathematics, ISSN 0973-1768, Volume 8,
Number 2, pp. 167-173.
[23]Tarig M. Elzaki, and Eman M. A. Hilal, (2012). Homotopy Perturbation
and Elzaki Transform for Solving Nonlinear Partial Differential Equations,
Mathematical Theory and Modeling , ISSN 2224-5804, Vol.2, No.3, 2012,
pp. 33-42.