- - - Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P. O. Box ۴۱۳۳۵-۱۹۱۴, Guilan, Rasht, Iran.
- - - Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran.
- - - Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P. O. Box ۴۱۳۳۵-۱۹۱۴, Guilan, Rasht, Iran.

determination of eigenvalues and eigenfunctions of a High-order Sturm-Liouville problem (HSLP) is considered. To this end, the Differential Transformation Method (DTM) is applied which is an efficient technique for solving differential equations. The results of the proposed approach are compared with those of some well-known methods reported in the literature. Four illustrative real life examples of mechanical engineering are provided to show the ability and the cost-effectiveness of this numerical approach.

High order sturm-liouville problems, Differential transformation method, eigenvalue