Solutions of the system of differential equations by differential transform method. (English) Zbl 1032.35011

Summary: In this study, three-dimensional differential transform method has been introduced and fundamental theorems have been defined for the first time. Moreover, as an application of two and three-dimensional differential transform, exact solutions of linear and non-linear systems of partial differential equations have been investigated. The results of the present method are compared very well with those obtained by decomposition method. Differential transform method can easily be applied to linear or non-linear problems and reduces the size of computational work. With this method exact solutions may be obtained without any need of cumbersome work and it is an useful tool for analytical and numerical solutions.


35A22 Transform methods (e.g., integral transforms) applied to PDEs
35C05 Solutions to PDEs in closed form
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[1] Debnath, L., Nonlinear Partial Differential Equations for Scientists and Engineers (1997), Birkhauser: Birkhauser Boston, MA · Zbl 0892.35001
[2] Logan, J. D., An Introduction to Nonlinear Partial Differential Equations (1994), Wiley-Interscience: Wiley-Interscience New York · Zbl 0834.35001
[3] Whitham, G. B., Linear and Nonlinear Waves (1974), Wiley: Wiley New York · Zbl 0373.76001
[4] Wazwaz, A. M., The decomposition method applied to systems of partial equations and to the reaction-diffusion Brusselator model, Appl. Math. Comput., 110, 251-264 (2000) · Zbl 1023.65109
[5] Zhou, J. K., Differential Transformation and Its Application for Electrical Circuits (1986), Huazhong University Press: Huazhong University Press Wuhan, China, (in Chinese)
[6] Chen, C. K.; Ho, S. H., Solving partial differential equations by two dimensional differential transform, Appl. Math. Comput., 106, 171-179 (1999) · Zbl 1028.35008
[7] Jang, M. J.; Chen, C. L.; Liu, Y. C., Two-dimensional differential transform for partial differential equations, Appl. Math. Comput., 121, 261-270 (2001) · Zbl 1024.65093
[8] F. Ayaz, On the two-dimensional differential transform method, Appl. Math. Comput., in press; F. Ayaz, On the two-dimensional differential transform method, Appl. Math. Comput., in press · Zbl 1023.35005
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