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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.

35A22Transform methods (PDE)
35G25Initial value problems for nonlinear higher-order PDE
35C10Series solutions of PDE
Full Text: DOI
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