Abstract
Bu makale, Dirichlet sınır şartlarıyla ve -y''(x)+q(x)y(x) diferansiyel ifadeyle üretilen Sturm Liouville diferansiyel operatörleriyle ilgilidir. Burada q(x) sonlu sayıda tekil noktaları olan Lebesque integrallenebilir potansiyel fonksiyondur. Nümerik yöntemlerden sonlu farklar yöntemi kullanılarak, Sturm Liouville diferansiyel operatörün özdeğerleri elde edilmiştir. Bu özdeğerlerin perturbasyonları hesaplanmıştır.
Keywords
References
- BIRKHOFF, G.D., "Boundary Value and Expansion Problems of Ordinary Linear Differantial Equations", Trans. Amer. Math. Soc., 9, 373-395, 1908.
- TAMARKIN, J. D., "Some General Problems of the Theory of Ordinary Linear Differential Equations and Expansion of an Arbitrary Function in Series of Fundamental Functions", Math. Zeit., 27, 1-54, 1927.
- TITCHMARSH, E.C., "Eigenfunction Expansions", Oxford University Press, Vol I., 1962.
- NAIMARK, M. A., "Linear Differential Operators", 4th Edition, George G. Harrap and Company,1967.
- MARCHENKO, V. A., "Sturm-Liouville Operators and Applications", Basel, Birkhauser Verlag, 1986.
- EVERITT, W.N., Gunson, J., "Some Comments on Sturm-Liouville Eigenvalue Problems with Interior Singularities", Journal of Applied Mathematics and Physics., 38, 813-838, 1987.
- PARLETT, B. N., "The Symmetric Eigenvalue Problem", Englewood Cliffs, Prentice-Hall, N. J., 1980.
- DUNFORD, N., SCHWARTZ, J. T., "Linear Operators", Part 3, Spectral Operators, Wiley-Interscience, MR g:47001c, New York, 1988.
- PAINE, J. W., HOOG, F. R., ANDERSSEN R.S., "On the Correction of Finite Difference Eigenvalue Approximations For Sturm-Liouville Problems", Computing, 26, 123-139, 1981.
- ANDREW, A., PAINE J., "Correction of Finite Element Estimates For Sturm-Liouville Eigenvalues", Numer. Math.,50, 205-215, 1986.
Abstract
This paper relates to Sturm Liouville differential operators generated by the differential expression -y''(x)+q(x)y(x) and by Dirichlet boundary conditions. Here q(x) is a Lebesque integrable potential function having finite number of singular points. Using the finite difference method from numerical methods, eigenvalues of the Sturm Liouville differential operator are obtained. Perturbations of these eigenvalues are calculated.
References
- BIRKHOFF, G.D., "Boundary Value and Expansion Problems of Ordinary Linear Differantial Equations", Trans. Amer. Math. Soc., 9, 373-395, 1908.
- TAMARKIN, J. D., "Some General Problems of the Theory of Ordinary Linear Differential Equations and Expansion of an Arbitrary Function in Series of Fundamental Functions", Math. Zeit., 27, 1-54, 1927.
- TITCHMARSH, E.C., "Eigenfunction Expansions", Oxford University Press, Vol I., 1962.
- NAIMARK, M. A., "Linear Differential Operators", 4th Edition, George G. Harrap and Company,1967.
- MARCHENKO, V. A., "Sturm-Liouville Operators and Applications", Basel, Birkhauser Verlag, 1986.
- EVERITT, W.N., Gunson, J., "Some Comments on Sturm-Liouville Eigenvalue Problems with Interior Singularities", Journal of Applied Mathematics and Physics., 38, 813-838, 1987.
- PARLETT, B. N., "The Symmetric Eigenvalue Problem", Englewood Cliffs, Prentice-Hall, N. J., 1980.
- DUNFORD, N., SCHWARTZ, J. T., "Linear Operators", Part 3, Spectral Operators, Wiley-Interscience, MR g:47001c, New York, 1988.
- PAINE, J. W., HOOG, F. R., ANDERSSEN R.S., "On the Correction of Finite Difference Eigenvalue Approximations For Sturm-Liouville Problems", Computing, 26, 123-139, 1981.
- ANDREW, A., PAINE J., "Correction of Finite Element Estimates For Sturm-Liouville Eigenvalues", Numer. Math.,50, 205-215, 1986.
Details
| Other ID | JA44HG98KV |
|---|---|
| Journal Section | Articles |
| Authors | |
| Publication Date | July 11, 2016 |
| Submission Date | July 11, 2016 |
| Published in Issue | Year 2013 Volume: 2 Issue: 2 |