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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:

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 |

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\textit{I. H. Abdel-Halim Hassan}, Appl. Math. Comput. 129, No. 2--3, 183--201 (2002; Zbl 1026.34010)

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### References:

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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.