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Zbl 1026.34010
Abdel-Halim Hassan, I.H.
Different applications for the differential transformation in the differential equations. (English)
[J] Appl. Math. Comput. 129, No.2-3, 183-201 (2002). ISSN 0096-3003

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 2000:: *34A25 Analytical theory of ODE
34L16 Numerical approximation of eigenvalues, etc.
35A22 Transform methods (PDE)

Keywords: eigenvalue problems; normalized eigenfunctions; difference equations

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Zentralblatt MATH Berlin [Germany]