Solving partial differential equations by two-dimensional differential transform method

摘要

Using two-dimensional differential transform to solve Partial Differential Equations (PDE) is proposed in this study. First, the theory of two-dimensional differential transform is introduced. Second, taking 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 very well with those obtained by other analytical or approximate methods.