Different applications for the differential transformation in the differential equations. (English) Zbl 1026.34010

Abdel-Halim Hassan, I. H.

Appl. Math. Comput. 129, No. 2-3, 183-201 (2002).

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:

34A25	Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
34L16	Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators
35A22	Transform methods (e.g., integral transforms) applied to PDEs

Keywords:

eigenvalue problems; normalized eigenfunctions; difference equations

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