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Different applications for the differential transformation in the differential equations. (English) Zbl 1026.34010
Summary: A differential transformation technique which is applied to solve eigenvalue problems and to solve partial differential equations (PDE) is proposed in this study. First, using the one-dimensional differential transformation to construct the eigenvalues and the normalized eigenfunctions for differential equations of second and fourth order. Second, using the two-dimensional differential transformation to solve PDEs of 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.
MSC:
34A25Analytical theory of ODE (series, transformations, transforms, operational calculus, etc.)
34L16Numerical approximation of eigenvalues and of other parts of the spectrum
35A22Transform methods (PDE)