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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 697013, 21 pages
http://dx.doi.org/10.1155/2012/697013
Research Article

A New Approach for Linear Eigenvalue Problems and Nonlinear Euler Buckling Problem

Department of Mathematics, Faculty of Science, Dokuz Eylul University, 35160 Tinaztepe, Buca, Izmir, Turkey

Received 12 March 2012; Accepted 11 April 2012

Academic Editor: Allaberen Ashyralyev

Copyright © 2012 Meltem Evrenosoglu Adiyaman and Sennur Somali. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We propose a numerical Taylor's Decomposition method to compute approximate eigenvalues and eigenfunctions for regular Sturm-Liouville eigenvalue problem and nonlinear Euler buckling problem very accurately for relatively large step sizes. For regular Sturm-Liouville problem, the technique is illustrated with three examples and the numerical results show that the approximate eigenvalues are obtained with high-order accuracy without using any correction, and they are compared with the results of other methods. The numerical results of Euler Buckling problem are compared with theoretical aspects, and it is seen that they agree with each other.