Different applications for the differential transformation in the differential equations

摘要

The differential transformation technique which is applied to solve eigenvalue problems and to solve partial differential equations (P.D.E.) is proposed in this study. First, using the one-dimensional differential transformation to construct the eigenvalues and the normalized eigenfunctions for the differential equation of the second- and the fourth-order. Second, using the two-dimensional differential transformation to solve P.D.E. of the first- and second-order with constant coefficients. In both cases, a set of difference equations is derived and the calculated results are compared closely with the results obtained by other analytical methods.