On the two-dimensional differential transform method. (English) Zbl 1023.35005

Summary: In this paper, the two-dimensional differential transform method of the solution of the initial value problem for partial differential equations (PDEs) has been studied. New theorems have been added and some linear and nonlinear PDEs solved by using this method. The method can be easily applied to linear or nonlinear problems and is capable of reducing the size of computational work. In this work, additionally, analytical form solutions of two diffusion problems have been obtained and the solutions are compared with those obtained by the decomposition method.


35A22 Transform methods (e.g., integral transforms) applied to PDEs
35G25 Initial value problems for nonlinear higher-order PDEs
35C10 Series solutions to PDEs
Full Text: DOI


[1] Zhou, J. K., Differential Transformation and its Application for Electrical Circuits (1986), Huazhong University Press: Huazhong University Press Wuhan, China, (in Chinese)
[2] 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
[3] 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
[4] Wazwaz, A. M., Exact solutions to nonlinear diffusion equations obtained by the decomposition method, Appl. Math. Comput., 123, 109-122 (2001) · Zbl 1027.35019
[5] Saied, E. A., The non-classical solution of the inhomogeneous non-linear diffusion equation, Appl. Math. Comput., 98, 103-108 (1999) · Zbl 0929.35065
[6] Saied, E. A.; Hussein, M. M., New classes of similarity solutions of the inhomogeneous nonlinear diffusion equations, J. Phys. A, 27, 4867-4874 (1994) · Zbl 0842.35002
[7] Dresner, L., Similarity Solutions of Nonlinear Partial Differential Equations (1983), Pitman: Pitman New York · Zbl 0526.35002
[8] Zachmanoglou, E. C.; Thoe, D. W., Introduction to Partial Differential Equations with Applications (1976), Dover: Dover New York · Zbl 0327.35001
[9] Strauss, W. A., Partial Differential Equations an Introduction (1992), John Wiley: John Wiley Singapore · Zbl 0817.35001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.