A new algorithm for calculating two-dimensional differential transform of nonlinear functions

A new algorithm for calculating the two-dimensional differential transform of nonlinear functions is developed in this paper. This new technique is illustrated by studying suitable forms of nonlinearity. Three strongly nonlinear partial differential equations are then solved by differential transform method to demonstrate the validity and applicability of the proposed algorithm. The present framework offers a computationally easier approach to compute the transformed function for all forms of nonlinearity. This gives the technique much wider applicability.

[1]  Bor-Lih Kuo.  Thermal boundary-layer problems in a semi-infinite flat plate by the differential transformation method , 2004, Appl. Math. Comput..

[2]  Abdul-Majid Wazwaz,et al.  Adomian decomposition method for a reliable treatment of the Bratu-type equations , 2005, Appl. Math. Comput..

[3]  Cha’o-Kuang Chen,et al.  Application of Taylor transformation to optimize rectangular fins with variable thermal parameters , 1998 .

[4]  Chieh-Li Chen,et al.  Application of Taylor transformation to nonlinear predictive control problem , 1996 .

[5]  Robert D. Russell,et al.  Numerical solution of boundary value problems for ordinary differential equations , 1995, Classics in applied mathematics.

[6]  Chieh-Li Chen,et al.  Differential transformation technique for steady nonlinear heat conduction problems , 1998, Appl. Math. Comput..

[7]  B.-L. Kuo,et al.  Application of the differential transformation method to the solutions of Falkner-Skan wedge flow , 2003 .

[8]  S. M. Roberts,et al.  On the closed form solution of Troesch's problem , 1976 .

[9]  Ming-Jyi Jang,et al.  Analysis of the response of a strongly nonlinear damped system using a differential transformation technique , 1997 .

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

[11]  Chao-Kuang Chen,et al.  Application of the differential transformation method to a non-linear conservative system , 2004, Appl. Math. Comput..

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

[13]  Cha'o-Kuang Chen,et al.  Solving partial differential equations by two-dimensional differential transform method , 1999, Appl. Math. Comput..

[14]  Chen Cha'o-Kuang,et al.  The solution of the blasius equation by the differential transformation method , 1998 .

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