Oscillation theory and numerical solution of sixth order Sturm-Liouville problems

SIAM Journal on Numerical Analysis

Volumn 35, Issue 5, 1998, Pages 2070-2098

  Greenberg, Leon ^a   Marletta, Marco ^b  

^a University of Maryland   (United States)

^b UNIVERSITY OF LEICESTER   (United Kingdom)

Author keywords

Homotopy; Oscillation theory; Riccati variables; Sixth order ODE eigenproblem

Indexed keywords

EID: 0042776260     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142997316451     Document Type: Article

References (11)

1. F. ATKINSON, Discrete and Continuous Boundary Problems, Academic Press, New York, 1964.
2. S. CHANDRASEKHAR, On characteristic value problems in high order differential equations which arise in studies on hydrodynamic and hydromagnetic stability, in Proc. Symp. Special Topics in Applied Mathematics, Amer. Math. Monthly, 61 (1955), pp. 32-45.
3. P. G. DRAZIN AND W. H. REID, Hydrodynamic stability, Cambridge University Press, Cambridge, 1981.
4. C. T. FULTON, S. PRUESS, AND L. WU, A Sturm separation theorem for a linear 2nth order selfadjoint differential equation, J. Appl. Math. Stochastic Anal., 8 (1995), pp. 29-26.
5. G. GOLUB AND C. F. VAN LOAN, Matrix Computations, The Johns Hopkins University Press, Baltimore, MD, 1991.
6. L. GREENBERG, A Prüfer Method for Calculating Eigenvalues of Self adjoint Systems of Ordinary Differential Equations, Parts 1 and 2, Tech. report TR91-24, Department of Mathematics, University of Maryland, College Park, MD, 1991.
7. L. GREENBERG AND M. MARLETTA, Oscillation theory and numerical solution of fourth order Sturm-Liouville problems, IMA J. Numer. Anal., 15 (1995), pp. 319-356.
8. L. GREENBERG AND M. MARLETTA, Richardson Extrapolation and the Solution of Fourth Order Sturm-Liouville Problems by Approximation of the Coefficients, Tech. report 1995/8, University of Leicester, Department of Mathematics and Computer Science, Leicester, UK, 1995.
9. L. GREENBERG AND M. MARLETTA, The code SLEUTH for solving fourth order Sturm-Liouville problems, ACM Trans. Math. Software, 23(1997), pp. 453-493.
10. C. R. MAPLE, Special Numerical Methods and a Parallel Algorithm for Hamiltonian Eigen-problems, Ph.D. thesis, Department of Mathematics and Computer Science, University of Leicester, Leicester, UK, 1998.
11. W. T. REID, Sturmian Theory for Ordinary Differential Equations, Springer-Verlag, New York, 1980.