## Solving partial differential equations by two-dimensional differential transform method.(English)Zbl 1028.35008

Summary: Using the two-dimensional differential transform to solve Partial Differential Equations (PDE) is proposed in this study. First, the theory of the two-dimensional differential transform is introduced. Second, taking the two-dimensional differential transform of a PDE problem, a set of difference equations is derived. Doing some simple mathematical operations on these equations, we can get a closed form series solution or an approximate solution quickly. Finally, three PDE problems with constant and variable coefficients are solved by the present method. The calculated results are compared with those obtained by other analytical or approximate methods.

### MSC:

 35A22 Transform methods (e.g., integral transforms) applied to PDEs 35C05 Solutions to PDEs in closed form 35C10 Series solutions to PDEs
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### References:

 [1] J.K. Zhou, Differential Transformation and Its Applications for Electrical Circuits (in Chinese), Huazhong Univ. Press, Wuhan, China, 1986 [2] Chen, C.K.; Ho, S.H., Application of differential transformation to eigenvalue problems, Appl. math. comput., 79, 173-188, (1996) · Zbl 0879.34077 [3] F.B. Hildebrand, Advanced Calculus for Applications, Prentice-Hall, Englewood Cliffs, NJ, 1976, p. 387 · Zbl 0333.00003 [4] M.U. Tyn, L. Debnath, Partial Differential Equations for Scientists and Engineers, Elsevier, Amsterdam, 1988, p. 73 · Zbl 0644.35001 [5] H.F. Weinberger, A First Course in Partial Differential Equations with Complex Variables and Transform Methods, Blaisdell, New York, 1965, p. 384 · Zbl 0127.04805
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