Numerical methods for higher order Sturm-Liouville problems

Journal of Computational and Applied Mathematics

Volumn 125, Issue 1-2, 2000, Pages 367-383

  Greenberg, Leon ^a   Marletta, Marco ^b  

^a University of Maryland   (United States)

^b UNIVERSITY OF LEICESTER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

NUMERICAL METHODS; PROBLEM SOLVING; THEOREM PROVING;

DIFFERENTIAL STURM-LIOUVILLE BOUNDARY EIGENVALUE PROBLEMS;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 0034517078     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(00)00480-5     Document Type: Article

References (28)

1. F. Atkinson, Discrete and Continuous Boundary Problems, Academic Press, New York, 1964.
2. G.D. Birkhoff, On the asymptotic character of the solutions of certain linear differential equations containing a parameter, Trans. AMS 9 (1908) 219-223.
3. G.D. Birkhoff, Boundary value problems and expansion problems of ordinary differential equations, Trans. AMS 9 (1908) 373-395.
4. S. Blanes, F. Casas, J.A. Oteo, J. Ros, Magnus and Fer expansions for matrix differential equations: the convergence problem, J. Phys. A: Math. Gen. 31 (1998) 259-268.
5. S. Chandrasekhar, On characteristic value problems in high order differential equations which arise in studies on hydrodynamic and hydromagnetic stability, in Proceedings of the Symposium on Special Topics in Applied Mathematics, Amer. Math. Monthly 61 (2) (1955) 32-45.
6. E.B. Davies, Pseudospectra: the harmonic oscillator and complex resonances. Preprint, Department of Mathematics, King's College London, 1998.
7. L. Dieci, R.D. Russell, E.S. Van Vleck, Unitary integrators and applications to continuous orthonormalization techniques, SIAM J. Numer. Anal. 31 (1994) 261-281.
8. P.G. Drazin, W.H. Reid, Hydrodynamic Stability, Cambridge University Press, Cambridge, 1981.
9. C.I. Gheorghiu, I.S. Pop, A modified Chebyshev-tau method for a hydrodynamic stability problem. Approximation and Optimization: Proceedings of the International Conference on Approximation and Optimization (Romania) -ICAOR, Cluj-Napoca, July 29-August 1, 1996. Vol. II, 1997, pp. 119-126.
10. I.C. Gohberg, M.G. Krein, Introduction to the Theory of Linear Nonselfadjoint Operators, Trans. Math. Monographs 18 (1969).
11. L. Greenberg, A. Prüfer method for calculating eigenvalues of selfadjoint systems of ordinary differential equations, Parts 1 and 2, University of Maryland Technical Report TR91-24, 1991.
12. L. Greenberg, An oscillation method for fourth-order selfadjoint two-point boundary value problems with nonlinear eigenvalues, SIAM J. Math. Anal. 22 (1991) 1021-1042.
13. L. Greenberg, M. Marletta, Oscillation theory and numerical solution of fourth order Sturm-Liouville problems, IMA J. Numer. Anal. 15 (1995) 319-356.
14. L. Greenberg, M. Marletta, The code SLEUTH for solving fourth order Sturm-Liouville problems, ACM Trans. Math. Software 23 (1997) 453-493.
15. L. Greenberg, M. Marletta, Oscillation theory and numerical solution of sixth order Sturm-Liouville problems, SIAM J. Numer. Anal. 35 (1998) 2070-2098.
16. L. Greenberg, M. Marletta, Numerical solution of nonselfadjoint Sturm-Liouville problems and related systems, SIAM J. Numer. Anal., submitted.
17. A. Iserles, S.P. Nørsett, On the solution of linear differential equations in Lie groups, Philos. Trans. Roy. Soc. London A 357 (1999) 983-1019.
18. P. Kravanja, T. Sakurai, M. Van Barel, On locating clusters of zeros of analytic functions, Report TW280, Dept. of Computer Science, Katholieke Universiteit Leuven, Belgium, 1998.
19. W. Magnus, On the exponential solution of differential equations for a linear operator, Comm. Pure Appl. Math. 7 (1954) 649-673.
20. C.R. Maple, M. Marletta, Algorithms and software for selfadjoint ODE eigenproblems, in: D. Bainov (Ed.), Proceedings of the 8th International Colloquium on Differential Equations, VSP, Utrecht, 1998.
21. M. Marletta, Numerical solution of eigenvalue problems for Hamiltonian systems, Adv. Comput. Math. 2 (1994) 155-184.
22. M.A. Naimark, Linear Differential Operators, Vol. 1, Ungar, New York, 1968.
23. S.A. Orszag, Accurate solution of the Orr-Sommerfeld stability equation, J. Fluid Mech. 50 (1971) 689-703.
24. W.T. Reid, Sturmian Theory for Ordinary Differential Equations, Springer, New York, 1980.
25. M. Roseau, Vibrations in Mechanical Systems, Springer, Berlin, 1987.
26. B. Straughan, D.W. Walker, Two very accurate and efficient methods for computing eigenvalues and eigenfunctions in porous convection problems, J. Comput. Phys. 127 (1996) 128-141.
27. L.N. Trefethen, Pseudospectra of linear operators, SIAM Rev. 39 (1997) 383-406.
28. X. Ying, I.N. Katz, A reliable argument principle algorithm to find the number of zeros of an analytic function in a bounded domain, Numer. Math. 53 (1988) 143-163.