Functional-discrete Method for Eigenvalue Transmission Problem with Periodic Boundary Conditions

Computational Methods in Applied Mathematics

Volumn 5, Issue 2, 2005, Pages 201-220

  Makarov, V L ^a   Rossokhata, N O ^a   Bandyrskii B I ^b  

^a INSTITUTE OF MATHEMATICS   (Ukraine)

^b IVAN FRANKO NATIONAL UNIVERSITY OF LVIV   (Ukraine)

Author keywords

Basic Problem; Bessel Functions; Convergence Rate As A Geometric Series; Eigenvalue Transmission Problem; Functional Discrete Method; Matching Conditions; Periodic Boundary Conditions

Indexed keywords

EID: 34250351967     PISSN: 16094840     EISSN: 16099389     Source Type: Journal    
DOI: 10.2478/cmam-2005-0010     Document Type: Article

References (20)

1. G. Adam, S. Adam, and A. Corciovei, Local and accumulated truncation errors in a class of perturbative numerical methods, Rev. Routirane Phys., 25 (1980), pp. 39-53.
2. A. L. Andrew, Computation of higher Sturm-Liouville eigenvalues, in: Congressus Numeratium (P. S. Meek and G. H. J. van Ries, eds.), vol. 34, 1982, pp. 3-16.
3. A. L. Andrew, F. R. de Hoog, and P. I. Robb, Leighton's bounds for Sturm-Liouville eigenvalues, J. Math. Anal. Appl., 83 (1981), pp. 11-19.
4. B. I. Bandyrskii, V. L. Makarov, and O. L. Ukhanev, Sufficient conditions for convergence of nonclassic assimptotical series for the Sturm-Liouville problem with periodic conditions, Differ. Uravn., 35 (1999), no. 3, pp. 267-278, in Russian.
5. I. Dahnn, Anwendung eines direkten Verfahrens zur numerishen Behaudbung von Selbstadjungierten, positiv definiten Eigenwertaufgaben bei linearen gewehnlichen Differentialgleichungen mit stickweise stetigen Koeffizientenfunktionen, ZAMM, 62 (1982), pp. 687-695.
6. I. Dahnn, A. Kastelewicz, and G. Schalm, Zur numerischen Berechnung der Eigenwerte und Eigenfunktionen der Hillschen Differentialgleichung mit periodischen Randbedingangen, Wiss. Z. Humboldt Univ. Berlin Math. Natur. Reiche., 28 (1979), pp. 495-504.
7. R. G. Gordon, New methods for constructing wave functions for bound states and scattering, J. Chem. Phys., 51 (1969), pp. 14-25.
8. L. G. Ixary, M. I. Cristu, and M. S. Popa, Choosing step sizes for perturbative methods to solve the S'chrodinger equation, J. Comput. Phys., 36 (1980), pp. 170-181.
9. N. Kryloff and N. Bogoliouboff, Sopra id metodo del coefficient costanti (metodo del tronconi) per l'integrazione approssimate della equazioni differenziali della Fisica Matematica, Bolletino della Unione Matematica Italiana, 7 (1926), no. 2.
10. W. Leighton, Upper and lower bounds for eigenvalues, J. Math. Anal. Appl., 35 (1971), pp. 381-388.
11. V. Makarov, N. Rossokhata, and B. Bandyrskii, Functional-discrete method with high order of accuracy for eigenvalue transmission problem, Comput. Meth. Appl. Math., 4 (2004), no. 3, pp. 324-349.
12. V. L. Makarov, About the functional-discrete method of arbitrary order of accuracy for solving the Sturm-Liouville problem with piecewise smooth coefficients, Dokl. Akad. Nauk SSSR, 320 (1991), no. 1, pp. 34-39, in Russian.
13. V. L. Makarov, About the functional-discrete approach for solving problems of mathematical physics, in: Proc. of Wekua workshop, Tbilisi, 1993, pp. 44-51, in Russian.
14. V. L. Makarov, FD-method: the exponential rate of convergence, J. Math. Scienc., 104 (1997), no. 6, pp. 1648-1653.
15. V. L. Makarov and O. L. Ukhanev, FD-method for the Sturm-Liouville problems. Exponential rate of convergence, in: Appl. Math. Inform., vol. 2, Tbilisi University Press, Tbilisi, 1997, pp. 1-19.
16. J. W. Paine, Correction of Sturm-Liouville eigenvalue estimates, Math. Comput., 39 (1982), pp. 415-420.
17. J. W. Paine and A. L. Andrew, Bounds and high-order estimates for Sturm-Liouville eigenvalues, J. Math. Anal. Appl., 96 (1983), pp. 388-394.
18. S. A. Pruess, Estimating the eigenvalues of the Sturm-Liouville problems by approximating the differential equations, Ph.D. thesis, Purdue University, 1970.
19. J. D. Pryce, Numerical solution of Sturm-Liouville problems, Calendon Press, Oxford - New York - Tokyo, 1993.
20. A. N. Tikhonov and A. A. Samarskii, Homogeneous difference schemes, Dokl. Akad. Nauk SSSR, 122 (1958), no. 4, pp. 562-565.