Homotopy Perturbation and Elzaki Transform for Solving Nonlinear Partial Differential Equations

In this work, we present a reliable combination of homotopy perturbation method and Elzaki transform to investigate some nonlinear partial differential equations. The nonlinear terms can be handled by the use of homotopy perturbation method. The proposed homotopy perturbation method is applied to the reformulated first and second order initial value problem which leads the solution in terms of transformed variables, and the series solution is obtained by making use of the inverse transformation. The results show the efficiency of this method. Keywords : Homotopy perturbation methods, Elzaki transform nonlinear partial differential equations.

[1]  T. Elzaki,et al.  ON THE ELZAKI TRANSFORM AND ORDINARY DIFFERENTIAL EQUATION WITH VARIABLE COECIENTS , 2011 .

[2]  T. Elzaki,et al.  ON THE CONNECTIONS BETWEEN LAPLACE AND ELZAKI TRANSFORMS , 2011 .

[3]  Nuran Güzel,et al.  SOLUTION OF SHIFF SYSTEMS BY USING DIFFERENTIAL TRANSFORM METHOD , 2008 .

[4]  A. Kılıçman,et al.  An application of double Laplace transform and double Sumudu transform , 2009 .

[5]  Adem Kilicman,et al.  A NOTE ON THE SUMUDU TRANSFORMS AND DIFFERENTIAL EQUATIONS , 2010 .

[6]  Giriraj Methi,et al.  Applications of Homotopy Perturbation Method to Partial Differential Equations , 2011 .

[7]  M. Jafari,et al.  Improved Homotopy Perturbation Method , 2010 .

[8]  E. S. Ismail,et al.  Accuracy of the Adomian decomposition method applied to the Lorenz system , 2006 .

[9]  Jun Zhang,et al.  A Sumudu based algorithm for solving differential equations , 2007, Comput. Sci. J. Moldova.

[10]  Tarig M. Elzaki,et al.  Elzaki and Sumudu Transforms for Solving some Differential Equations , 2012 .

[11]  Devendra Kumar,et al.  Homotopy Perturbation Sumudu Transform Method for Nonlinear Equations , 2011 .

[12]  Nasser Hassan Sweilam,et al.  Exact solutions of some coupled nonlinear partial differential equations using the homotopy perturbation method , 2009, Comput. Math. Appl..

[13]  Shih-Hsiang Chang,et al.  A new algorithm for calculating one-dimensional differential transform of nonlinear functions , 2008, Appl. Math. Comput..

[14]  Shih-Hsiang Chang,et al.  A new algorithm for calculating two-dimensional differential transform of nonlinear functions , 2009, Appl. Math. Comput..

[15]  T. Elzaki.  THE NEW INTEGRAL TRANSFORM ELZAKI TRANSFORM , 2011 .

[16]  A. Kılıçman,et al.  A NOTE ON INTEGRAL TRANSFORM AND PARTIAL DIFFERENTIAL EQUATION , 2010 .

[17]  A. Kılıçman,et al.  ON SOME APPLICATIONS OF A NEW INTEGRAL TRANSFORM , 2010 .