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.


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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