- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 697013, 21 pages
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.
- J. D. Pryce, Numerical Solution of Sturm-Liouville Problems, Monographs on Numerical Analysis, The Clarendon Press Oxford University Press, New York, NY, USA, 1993.
- I. Stakgold, “Branching of solutions of nonlinear equations,” SIAM Review, vol. 13, pp. 289–332, 1971.
- R. M. Jones, Buckling of Bars, Plates, and Shells, Bull Ridge, Virginia, Va, USA, 2006.
- G. Domokos and P. Holmes, “Euler's problem, Euler's method, and the standard map; or, The discrete charm of buckling,” Journal of Nonlinear Science, vol. 3, no. 1, pp. 109–151, 1993.
- D. H. Griffel, Applied Functional Analysis, Ellis Horwood Series in Mathematics and Its Applications, Ellis Horwood, Chichester, UK, 1981.
- L. Euler, “Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes ostwald’s klassiker der exakten wiss,” Laussane and Geneva, vol. 75, 1774.
- M. E. Adiyaman and S. Somali, “Taylor's decomposition on two points for one-dimensional Bratu problem,” Numerical Methods for Partial Differential Equations, vol. 26, no. 2, pp. 412–425, 2010.
- A. Ashyralyev and P. E. Sobolevskii, New difference schemes for partial differential equations, vol. 148 of Operator Theory: Advances and Applications, Birkhäuser, Basel, Switzerland, 2004.
- N. M. Bujurke, C. S. Salimath, and S. C. Shiralashetti, “Computation of eigenvalues and solutions of regular Sturm-Liouville problems using Haar wavelets,” Journal of Computational and Applied Mathematics, vol. 219, no. 1, pp. 90–101, 2008.
- A. L. Andrew, “Asymptotic correction of Numerov's eigenvalue estimates with natural boundary conditions,” Journal of Computational and Applied Mathematics, vol. 125, no. 1-2, pp. 359–366, 2000.
- B. van Brunt, The Calculus of Variations, Universitext, Springer, New York, NY, USA, 2004.
- R. S. Anderssen and F. R. de Hoog, “On the correction of finite difference eigenvalue approximations for Sturm-Liouville problems with general boundary conditions,” BIT Numerical Mathematics, vol. 24, no. 4, pp. 401–412, 1984.
- S. Somali and V. Oger, “Improvement of eigenvalues of Sturm-Liouville problem with -periodic boundary conditions,” Journal of Computational and Applied Mathematics, vol. 180, no. 2, pp. 433–441, 2005.
- V. Mehrmann and A. Miedlar, “Adaptive computation of smallest eigenvalues of self-adjoint elliptic partial differential equations,” Numerical Linear Algebra with Applications, vol. 18, no. 3, pp. 387–409, 2011.
- Q.-M. Cheng, T. Ichikawa, and S. Mametsuka, “Estimates for eigenvalues of the poly-Laplacian with any order in a unit sphere,” Calculus of Variations and Partial Differential Equations, vol. 36, no. 4, pp. 507–523, 2009.
- C. Lovadina, M. Lyly, and R. Stenberg, “A posteriori estimates for the Stokes eigenvalue problem,” Numerical Methods for Partial Differential Equations, vol. 25, no. 1, pp. 244–257, 2009.
- S. Jia, H. Xie, X. Yin, and S. Gao, “Approximation and eigenvalue extrapolation of biharmonic eigenvalue problem by nonconforming finite element methods,” Numerical Methods for Partial Differential Equations, vol. 24, no. 2, pp. 435–448, 2008.
- C. V. Verhoosel, M. A. Gutiérrez, and S. J. Hulshoff, “Iterative solution of the random eigenvalue problem with application to spectral stochastic finite element systems,” International Journal for Numerical Methods in Engineering, vol. 68, no. 4, pp. 401–424, 2006.