Reduced Differential Transform Method for Partial Differential Equations

Recently differential transform method (DTM) has been used to solve various partial differential equations. In this paper, an alternative approach called the reduced differential transform method (RDTM) is presented to overcome the demerit of complex calculation of differential transform method. Comparing the methodology with some known techniques shows that the present approach is effective and powerful. In addition, three test problems of mathematical physics are discussed to illustrate the effectiveness and the performance of the reduced differential transform method.

[1]  Cha'o-Kuang Chen,et al.  Application of differential transformation to eigenvalue problems , 1996 .

[2]  Dogan Kaya,et al.  An application for a generalized KdV equation by the decomposition method , 2002 .

[3]  Ji-Huan He,et al.  Homotopy perturbation method: a new nonlinear analytical technique , 2003, Appl. Math. Comput..

[4]  Necdet Bildik,et al.  Two-dimensional differential transform method, Adomian's decomposition method, and variational iteration method for partial differential equations , 2006, Int. J. Comput. Math..

[5]  I. H. Abdel-Halim Hassan,et al.  Comparison differential transformation technique with Adomian decomposition method for linear and nonlinear initial value problems , 2008 .

[6]  Magdy A. El-Tawil,et al.  Solving nonlinear partial differential equations using the modified variational iteration Padé technique , 2007 .

[7]  George Adomian,et al.  Solving Frontier Problems of Physics: The Decomposition Method , 1993 .

[8]  David J. Evans,et al.  The numerical solution of multidimensional partial differential equations by the decomposition method , 2003, Int. J. Comput. Math..

[9]  Aydin Kurnaz,et al.  Approximate Solutions of Generalized Pantograph Equations by the Differential Transform Method , 2007 .

[10]  Aydin Kurnaz,et al.  n-Dimensional differential transformation method for solving PDEs , 2005, Int. J. Comput. Math..

[11]  Ji-Huan He.  Variational iteration method – a kind of non-linear analytical technique: some examples , 1999 .

[12]  Ming-Jyi Jang,et al.  Two-dimensional differential transform for partial differential equations , 2001, Appl. Math. Comput..

[13]  Fatma Ayaz,et al.  On the two-dimensional differential transform method , 2003, Appl. Math. Comput..

[14]  Necdet Bildik,et al.  The Use of Variational Iteration Method, Differential Transform Method and Adomian Decomposition Method for Solving Different Types of Nonlinear Partial Differential Equations , 2006 .