Random Articles
Reseach Article
On Rayleigh-Ritz Method in Three-Parameter Eigenvalue Problems
| International Journal of Computer Applications |
| Foundation of Computer Science (FCS), NY, USA |
| Volume 86 - Number 3 |
| Year of Publication: 2014 |
| Authors: Surashmi Bhattacharyya, Arun Kumar Baruah |
10.5120/14969-3149
|
Surashmi Bhattacharyya, Arun Kumar Baruah . On Rayleigh-Ritz Method in Three-Parameter Eigenvalue Problems. International Journal of Computer Applications. 86, 3 ( January 2014), 38-42. DOI=10.5120/14969-3149
Abstract
This paper deals with the computation of the eigenvalues of a three-parameter Sturm-Liouville problem in the form of ordinary differential equation using Rayleigh-Ritz Method, a method which is based on the principle of variational methods. This method has been effective in computing the eigenvalues of self-adjoint problems. The resulting equations obtained in applying Rayleigh-Ritz method on the problem are solved to find the rough estimates of the eigenvalues of the problem. Rough estimates are used as starting approximations in the corresponding shooting method to obtain their actual values.
References
- Arscott, F. M. 1962. Two-parameter eigenvalue problems in differential equation. Mathematics research center, United States Army, The University of Wisconsin.
- Atkinson, F. V. 1968. Multiparameter spectral theory, Bull. Am. Math. Soc. , 75, (1-28).
- Sleeman, B. D. 1972. The two-parameter Sturm-Liouville problem for ordinary differential equations, II, Proc. of the American Math. Soc vol. 34(1), 165-170.
- Browne, P. J. 1972. A multiparameter eigenvalue problem, J. Math. Analysis and Appl. , 38, 553-568.
- Baruah, A. K. 1987. Estimation of eigen elements in a two- parameter eigenvalue problem, Ph. D. Thesis, Dibrugarh University, Assam.
- Baruah, A. K. 2012. Ritz method in multiparameter eigenvalue problem, IFRSA's International of Computing, Vol. 2(1), 156-162.
- Konwar, J. 2002. Certain studies of two-parameter eigenvalue problem, Ph. D. thesis, Dibrugarh University, Assam.
- Changmai, J. 2009. Study of two-parameter eigenvalue problem in the light of finite element procedure, Ph. D thesis, Dibrugarh University, Assam.
- Plestanjak, B. 2006. Multiparameter eigenvalue problems, 2nd International Conference on Structural Matrices, Hongkong Baptist University.
- Fox, L. , Hayes, L. And Mayers, D. F. 1972. The double eigenvalue problem : Topics in numerical analysis, Proc. Roy Irish Acad. Con. , Univ. College, Dublin, Academic Press, New York, London, 93-112.
- Chanane, B. , and Boucherif, A. 2012. Two-parameter Sturm-Liouville problems, ar Xiv:1208. 3695v1 [math. SP]. King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia.
- Gregus, M. , Nueman, F. and Arscott, F. M. 1971. Three point boundary value problems in differential equation, J, London Math. Soc(2),3, 429-436.
- Sleeman, B. D. , 1972. Completeness and expansion theorems for a two-parameter eigenvalue problem in ordinary differential equations using variational principles, J. , London Math. Soc. (2),6, 705-712.
- Jain, M. K. , 1983. Numerical solution of differential equations, Wiley Eastern Ltd. ,New-Delhi, 522-528.
- Sadiku, M. N. O. 2001. Numerical Techniques in Electromagnetics, CRC Press, 235-274.
- Collatz, L. 1968. Multiparameter eigenvalue problem in Inner Product Spaces , J. Compu. and Syst. Scie. , 2, 333-341.
- Rao, K. S. 2007. Numerical methods for scientists and engineers, Prentices-Hall of India(P) Ltd.
- Sastry, S. S. 2006. Introductory methods of numerical analysis, Prentices-Hall of India(P) Ltd.
Index Terms
Keywords