Aboodh, K. (2017). Homotopy Perturbation Method and Aboodh Transform for Solving Nonlinear Partial Differential Equations. Theory of Approximation and Applications, 11(1), 1-12.

Khalid Aboodh. "Homotopy Perturbation Method and Aboodh Transform for Solving Nonlinear Partial Differential Equations". Theory of Approximation and Applications, 11, 1, 2017, 1-12.

Aboodh, K. (2017). 'Homotopy Perturbation Method and Aboodh Transform for Solving Nonlinear Partial Differential Equations', Theory of Approximation and Applications, 11(1), pp. 1-12.

Aboodh, K. Homotopy Perturbation Method and Aboodh Transform for Solving Nonlinear Partial Differential Equations. Theory of Approximation and Applications, 2017; 11(1): 1-12.

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

^{}Department of Mathematics Omdurman Islamic University (http: //www. fst. oiu. edu. sd) sudan

Abstract

Here, a new method called Aboodh transform homotopy perturbation method (ATHPM) is used to solve nonlinear partial dierential equations, we present a reliable combination of homotopy perturbation method and Aboodh transform to investigate some nonlinear partial dierential equations. The nonlinear terms can be handled by the use of homotopy perturbation method. The results show the eciency of this method. Aboodh transform was introduced by Khalid Aboodh to facilitate the process of solving ordinary and partial differential equations in the time domain.

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

Authors [Persian]

Khalid Aboodh

^{}Department of Mathematics Omdurman Islamic University (http: //www. fst. oiu. edu. sd) sudan

Abstract [Persian]

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

[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.