Algorithm 810: The SLEIGN2 Sturm-Liouville code

ACM Transactions on Mathematical Software

Volumn 27, Issue 2, 2001, Pages 143-192

  Bailey, P B ^a   Everitt, W N ^b   Zettl, A ^a  

^a NORTHERN ILLINOIS UNIVERSITY   (United States)

^b UNIVERSITY OF BIRMINGHAM   (United Kingdom)

Author keywords

Algorithms; D.3.2 Programming Languages : Language Classifications FORTRAN 77; G.1.7 Numerical Analysis : Ordinary Differential Equations Boundary value problems; G.4 Mathematics of Computing : Mathematical Software; Sturm Liouville

Indexed keywords

EID: 0038594418     PISSN: 00983500     EISSN: None     Source Type: Journal    
DOI: 10.1145/383738.383739     Document Type: Article

References (37)

1. BAILEY, P. B. 1966. Sturm-Liouville eigenvalues via a phase function. SIAM J. Appl. Math. 14, 242-249.
2. BAILEY, P. B. 1976. SLEIGN: An eigenvalue-eigenfunction code for Sturm-Liouville problems. Rep. SAND77-2044. Sandia National Laboratories, Livermore, CA.
3. BAILEY, P. B. 1978. A slightly modified Prüfer transformation useful for calculating Sturm-Liouville eigenvalues. J. Comput. Phys. 29, 2, 306-310.
4. BAILEY, P. B. 1997. On the approximation of eigenvalues of Sturm-Liouville problems by those of suitably chosen regular ones. In Spectral Theory and Computational Methods of Sturm-Liouville Problems, Proceedings of the 1996 Barratt Lectures. Lecture Notes in Pure and Applied Mathematics (Knoxville, TN), D. Hinton and P. W. Schaefer, Eds. Marcel Dekker, Inc., New York, NY, 171-182.
5. BAILEY, P. B., EVERITT, W. N., WEIDMANN, J., AND ZETTL, A. 1993. Regular approximation of singular Sturm-Liouville problems. Results Math. 23, 1, 3-22.
6. BAILEY, P. B., EVERITT, W. N., AND ZETTL, A. 1991a. Computing eigenvalues of singular Sturm-Liouville problems. Results Math. 20, 391-423.
7. BAILEY, P. B., EVERITT, W. N., AND ZETTL, A. 1996. Regular and singular Sturm-Liouville problems with coupled boundary conditions. Proc. Roy. Soc. Edinburgh 126A, 505-514.
8. BAILEY, P. B., EVERITT, W. N., AND ZETTL, A. 1995. On the numerical computation of the spectrum of singular Sturm-Liouville problems. NSF Final Rep. for Grant DMS-9106470.
9. BAILEY, P. B., GARBOW, B. S., KAPER, H. G., AND ZETTL, A. 1991b. Eigenvalue and eigenfunction computations for Sturm-Liouville problems. ACM Trans. Math. Softw. 17, 4 (Dec.), 491-499.
10. BAILEY, P. B., GARBOW, B. S., KAPER, H. G., AND ZETTL, A. 1991c. ALGORITHM 700: A FORTRAN software package for Sturm-Liouville problems. ACM Trans. Math. Softw. 17, 4 (Dec.), 500-501.
11. BAILEY, P. B., GORDON, M. K., AND SHAMPINE, L. F. 1976. Solving Sturm-Liouville eigenvalues problems. Rep. SAND76-0560. Sandia National Laboratories, Livermore, CA.
12. BAILEY, P. B., GORDON, M. K., AND SHAMPINE, L. F. 1978. Automatic solution of the Sturm-Liouville problem. ACM Trans. Math. Softw. 4, 3 (Sept.), 193-208.
13. BIRKHOFF, G. AND ROTA, G.-C. 1969. Ordinary Differential Equations. Blaisdell Publishing Co., London, UK.
14. CIARLET, P., SCHULTZ, M., AND VARGA, R. 1968. Numerical methods for high-order accuracy for non linear boundary value problems; III: Eigenvalue problems. Numer. Math. 12, 120-133.
15. CODDINGTON, E. A. AND LEVINSON, N. 1995. Theory of Ordinary Differential Equations. McGraw-Hill, London, UK.
16. EASTHAM, M. S. P., KONG, Q., Wu, H., AND ZETTL, A. 1999. Inequalities among eigenvalues of Sturm-Liouville problems. J. Ineq. Appl. 3, 1, 25-43.
17. EVERITT, W. N. 1982. On the transformation theory of ordinary second-order symmetric differential equations. Czech. Math. J. 32 (107), 2, 275-306.
18. EVERITT, W. N., KWONG, M. K., AND ZETTL, A. 1983. Oscillations of eigenfunctions of weighted regular Sturm-Liouville problems. J. London Math. Soc. 27, 2, 106-120.
19. EVERITT, W. N., MÖLLER, M., AND ZETTL, A. 1997. Discontinuous dependence of the n-th Sturm-Liouville eigenvalue. In Proceedings of the International Conference on General Inequalities 7, C. Bandle, W. N. Everitt, L. Losonczi, and W. Walter, Eds. International Series of Numerical Mathematics. Birkhäuser-Verlag, Basel, Switzerland, 147-150.
20. EVERITT, W. N., MÖLLER, M., AND ZETTL, A. 1999. Sturm-Liouville problems and discontinous eigenvalues. Proc. Roy. Soc. Edinburgh 129A, 707-716.
21. KELLER, H. B. 1968. Numerical Methods for Two-Point Boundary Value Problems. Ginn-Blaisdell, Waltham, MA.
22. KELLER, H. B. 1976. Numerical Solution of Two Point Boundary Value Problems. SIAM, Philadelphia, PA.
23. KONG, Q., Wu, H., AND ZETTL, A. 1997. Dependence of eigenvalues on the problem. Math. Nachr. 188, 173-201.
24. KONG, Q., Wu, H., AND ZETTL, A. 1999. Dependence of the n-th Sturm-Liouville eigenvalue on the problem. J. Differ. Eq. 156, 238-354.
25. LITTLEWOOD, J. E. 1966. On linear differential equation sof the second order with a strongly oscillating coefficient of y. J. London Math. Soc. 41, 627-638.
26. MARLETTA, M. 1991. Certification of Algorithm 700: Numerical tests of the SLEIGN software for Sturm-Liouville problems. ACM Trans. Math. Softw. 17, 4 (Dec.), 481-490.
27. MCLEOD, J. B. 1968. Some examples of wildly oscillating potentials. J. London Math. Soc. 43, 647-654.
28. NAIMARK, M. A. 1968. Linear Differential Operators: II. Frederick Ungar, New York, NY. Translated from the 2nd Russian edition.
29. PRUESS, S. AND FULTON, C. T. 1993. Mathematical software for Sturm-Liouville problems. ACM Trans. Math. Softw. 19, 3 (Sept.), 360-376. Also available as NSF Final Report for Grants DMS88 and DMS88-00839.
30. PRYCE, J. D. 1986. The NAG Sturm-Liouville codes and some applications. NAG Newslett. 3, 4-26.
31. PRYCE, J. D. 1993. Numerical Solution of Sturm-Liouville Problems. Monographs on Numerical Analysis. Oxford University Press, Oxford, UK.
32. PRYCE, J. D. 1999. A test package for Sturm-Liouville solvers. ACM Trans. Math. Softw. 25, 1 (Mar.). This issue
33. TITCHMARSH, E. 1962. Eigenfunction Expansions Associated with Second Order Differential Equations, I. 2nd ed. Oxford University Press, Oxford, UK.
34. WEIDMANN, J. 1987. Spectral Theory of Ordinary Differential Operators. Springer Lecture Notes in Mathematics, vol. 1258. Springer-Verlag, Vienna, Austria.
35. ZETTL, A. 1993. Computing continous spectrum. In Proceedings of the International Symposium on Ordinary Differential Equations and Applications: Trends and Developments in Ordinary Differential Equations. World Scientific Publishing Co, Inc., Singapore, 393-406.
36. ZETTL, A. 1997. Sturm-Liouville problems. In Spectral Theory and Computational Methods of Sturm-Liouville Problems, Proceedings of the 1996 Barratt Lectures. Lecture Notes in Pure and Applied Mathematics (Knoxville, TN), D. Hinton and P. W. Schaefer, Eds. Marcel Dekker, Inc., New York, NY, 1-104.
37. ZETTL, A. 2001. Sturm-Liouville theory. Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL. Preprint.