Functional-discrete Method (FD-method) for Matrix Sturm-Liouville Problems

Computational Methods in Applied Mathematics

Volumn 5, Issue 4, 2005, Pages 362-386

  Bandyrskii, B I ^a   Gavrilyuk, I P ^b   Lazurchak, I I ^c   Makarov, V L ^d  

^a LVIV POLYTECHNIC NATIONAL UNIVERSITY   (Ukraine)

^b Staatliche Studienakademie Am Wartenberg 2   (Germany)

^c DROHOBYCH IVAN FRANKO STATE PEDAGOGICAL UNIVERSITY   (Ukraine)

^d INSTITUTE OF MATHEMATICS   (Ukraine)

Author keywords

a priori estimates; asymptotic expansions; Sturm Liouville problem with matrix coefficients

Indexed keywords

EID: 84989854430     PISSN: 16094840     EISSN: 16099389     Source Type: Journal    
DOI: 10.2478/cmam-2005-0017     Document Type: Article

References (13)

1. F. V. Atkinson, A. M. Krall, G. K. Leaf, and A. Zettl, On the numerical computation of eigenvalues of matrix Sturm-Liouville problems with matrix coefficients, Argon national laboratory reports, Darien, 1987.
2. B. Bandyrskii, I. Gavrylyuk, V. Makarov, and I. Makarov, Non-classical asymptotic expansions for eigenvalue problems with a parameter in the boundary conditions, Appl. Math. Inform. (Tbilisi University Press), 7 (2002), no. 1, pp. 35-77.
3. B. Bandyrskii, I. Lazurchak, and V. Makarov, A functional-discrete method for solving left-definite Sturm-Liouville problems with an eigenvalue parameter in the boundary conditions, Comput. Math. Math. Phys., 42 (2002), no. 5, pp. 646-659.
4. B. Bandyrskii and V. Makarov, Sufficient conditions for the eigenvalues operator -df/dx2 + q(x) with Ionkin-Samarskii to be real-valued, Comput. Math. Math. Phys., 40 (2000), no. 12, pp. 1715-1728.
5. B. Bandyrskii, V. Makarov, and O. L. Ukhanev, Sufficient conditions for the convergence of non-classical asymptotic expansions for Sturm-Liouville problems with periodic conditions, Differ. Equations, 35 (1999), no. 3, pp. 369-381.
6. H. I. Dwyer and A. Zettl, Eigenvalue computations for regular matrix Sturm-Liouville problems, Electron. J. Differ. Equ., (1995).
7. I. L. Makarov, Exact and truncated difference schemes for the vector Stur-Liouville problem, Vychisl. Prikl. Mat., Kiev, 49 (1983), pp. 72-84.
8. V. Makarov, N. Rossokhata, and B. Bandurskii, Functional-discrete method with a high order of accuracy for the eigenvalue transmission problem, Comput. Methods Appl. Math., 4 (2004), no. 3, pp. 324-349.
9. V. Makarov and O. L. Ukhanev, FD-method for Sturm-Liouville problems. Exponential rate of convergence, Appl. Math. Inform. (Tbilisi University Press), 2 (1997), pp. 1-19.
10. V. L. Makarov, On a functional-difference method of arbitrary order of precision for solving the Sturm Liouville problem with piecewise smooth coefficients, Sov. Math., Dokl., 44 (1991), no. 2, pp. 391-396.
11. V. L. Makarov, FD-method: The exponential rate of convergence, J. Math. Sci., New York, 104 (1997), no. 6, pp. 1648-1653.
12. V. L. Makarov, I. L. Makarov, and V. G. Prikazchikov, Exact difference and schemes of any order of accuracy for systems of second order differential equations, Differ. Uravn., 15 (1979), pp. 1194-1205.
13. G. Szego, Orthogonal Polynomials, American Mathematical Society, New York, 1959.