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Sturm-Liouville problems with impulse effects. (English) Zbl 1122.65378
Summary: This paper deals with the computation of the eigenvalues of Sturm-Liouville problems with several discontinuity conditions inside a finite interval and parameter dependent boundary conditions using the regularized sampling method. A few examples are worked out by computing several eigenvalues and their corresponding eigenfunctions.

65L15Eigenvalue problems for ODE (numerical methods)
34L16Numerical approximation of eigenvalues and of other parts of the spectrum
Full Text: DOI
[1] M.U. Akhmet, O. Ugur, The Sturm -- Liouville operator on the space of functions with discontinuity conditions.
[2] Amirov, R. Kh.: On Sturm -- Liouville operators with discontinuity conditions inside an interval. J. math. Anal. appl. 317, 163-176 (2006) · Zbl 1168.34019
[3] Boumenir, A.; Chanane, B.: Eigenvalues of S -- L systems using sampling theory. Appl. anal. 62, 323-334 (1996) · Zbl 0864.34073
[4] B. Chanane, Eigenvalues of Sturm Liouville problems with discontinuity conditions inside a finite interval, Appl. Math. Comput., in press, doi:10.1016/j.amc.2006.11.082. · Zbl 1124.65066
[5] Chanane, B.: Computation of the eigenvalues of Sturm -- Liouville problems with parameter dependent boundary conditions using the regularized sampling method. Math. comput. 74, No. 252, 1793-1801 (2005) · Zbl 1080.34010
[6] Chanane, B.: High order approximations of the eigenvalues of Sturm -- Liouville problems with coupled self-adjoint boundary conditions. Appl. anal. 80, 317-330 (2001) · Zbl 1031.34030
[7] Chanane, B.: High order approximations of the eigenvalues of regular Sturm -- Liouville problems. J. math. Anal. appl. 226, 121-129 (1998) · Zbl 0916.34029
[8] Dunford, N.; Schwartz, J. T.: Linear operators, part III. (1971) · Zbl 0243.47001
[9] Edmunds, E. E.; Evans, W. D.: Spectral theory and differential operators. (1987) · Zbl 0628.47017
[10] Hinton, D.; Schaefer, P. W.: Spectral theory and computational methods of Sturm -- Liouville problems. (1997) · Zbl 0866.00046
[11] O.Sh. Mukhtarov, Mahir Kadakal, Eigenvalues and normalized eigenfunctions of discontinuous Sturm -- Liouville problem with transmission conditions, Rep. Math. Phys., 54 (1), 41 -- 56. · Zbl 1092.34046
[12] Mukhtarov, O. Sh.; Yakubov, S.: Problems for differential equations with transmission conditions. Appl. anal. 81, 1033-1064 (2002) · Zbl 1062.34094
[13] Titeux, I.; Yakubov, S.: Completeness of root functions for thermal conduction in a strip with piecewise continuous coefficients. Math. mod. Meth. appl. Sci. 7, 1035-1050 (1997) · Zbl 0903.73008
[14] M.A. Naimark, Linear Differential Operators, Part I, Ungar, 1968. · Zbl 0227.34020
[15] Pryce, J. D.: Numerical solution of Sturm -- Liouville problems. (1993) · Zbl 0795.65053
[16] Wang, Aiping; Sun, Jiong; Gao, Pengfei: Completeness of eigenfunctions of Sturm -- Liouville problems with transmission conditions. J. spectral math. Appl. 1 (2005)
[17] Zayed, A. I.: Advances in Shannon’s sampling theory. (1993) · Zbl 0868.94011
[18] Zettl, A.: Adjoint and self-adjoint boundary value problems with interface conditions. SIAM J. Appl. math. 16, 851-859 (1968) · Zbl 0162.11201