**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30174

##### Two-dimensional Differential Transform Method for Solving Linear and Non-linear Goursat Problem

**Authors:**
H. Taghvafard,
G. H. Erjaee

**Abstract:**

**Keywords:**
Quadrature,
Spline interpolation,
Trapezoidal rule,
Numericalintegration,
Error analysis.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1062316

**References:**

[1] Zhou JK. Differential transform and its applications for electrical circuits. Wuhan. China: Huazhong University Press; 1986.

[2] Chen CL, Lin SH, Chen, CK. Application of Taylor transformation to nonlinear predictive control problem. Appl Math Model 1996;20:699- 710.

[3] Chiou JS, Tzeng JR. Application of the Taylor transform to non-linear vibration problems. ASME J Vib Acoust 1996;118:83-87.

[4] Jang MJ, Chen CL. Analysis of the response of a strongly non-linear damped system using a differential transformation technique. Appl Math Comput 1997;88:137-151.

[5] Chen CL, Liu YC. Differential transformation technique for steady nonlinear heat conduction problems. Appl Math Comput 1998;95:155- 164.

[6] Yu LT, Chen CK. The solution of the Blasius equation by the differential transformation method. Math Comput Model 1998; 28:101-111.

[7] Yu LT, Chen CK. Application of Taylor transformation to optimize rectangular fins with variable thermal parameters. Appl Math Model 1998;22:11-21.

[8] Kuo BL. Application of the differential transformation method to the solutions of Falkner-Skan wedge flow. Acta Mech 2003;164:161-174.

[9] Kuo BL. Thermal boundary-layer problems in a semi-infinite plate by the differential transformation method. Appl Math Comput 2004;150:303- 320.

[10] Chen CK, Chen SS. Application of the differential transformation method to a nonlinear conservative system. Appl Math Comput 2004;154:431-441.

[11] Chen CK, Ho SH. Solving partial differential equations by twodimensional differential transform. Appl Math Comput 1999;106:171- 179.

[12] Ayaz F. Solutions of the system of differential equations by differential transform method. Appl Math Comput 2004; 147:547-567.

[13] Ayaz F. Application of differential transform method to differentialalgebraic equations. Appl Math Comput 2004;152:649-657.

[14] Chen CK. Solving partial differential equations by two-dimensional differential transform. Appl Math Comput 1999;106:171-179.

[15] Jang MJ, Chen CK, Liu YC. Two-dimensional differential transform for partial differential equations. Appl Math Comput 2001;121:261-270.

[16] Wazwaz AM. On the numerical solution of the Goursat problem. Appl Math Comput 1993;59:89-95.

[17] Wazwaz AM. The decomposition method for approximate solution to the Goursat problem. Appl Math Comput 1995;69:299-311.

[18] Day JT. A Runge-Kutta method for the numerical solution of the Goursat problem in hyperbolic partial dfferential equations. Comput J 1966;9:81- 83.

[19] Evans DJ, Sanugi BB. Numerical solution of the Goursat problem by a nonlinear trapezoidal formula. Appl Math Lett 1988;1:221-223.

[20] Wazwaz AM. Partial Differential Equations: Methods and Applications, Balkema Publishers, The Netherlands, 2002.

[21] Wazwaz AM. The variational iteration method for a reliable treatment of the linear and the nonlinear Goursat problem. Appl Math Comput 2007;193:455-462.

[22] Chang SH, Chang IL. A new algorithm for calculating two-dimensional differential transform of nonlinear functions. Appl Math Comput 2009;215:2486-2494.

[23] Adomian G. Solving Frontier Problems of Physics: The Decomposition Method, Kluwer, Boston, 1994.