Algorithm 775: The Code SLEUTH for Solving Fourth-Order Sturm-Liouville Problems

ACM Transactions on Mathematical Software

Volumn 23, Issue 4, 1997, Pages 453-493

  Greenberg, Leon ^a   Marletta, Marco ^b  

^a Bldg 142   (United States)

^b UNIVERSITY OF LEICESTER   (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; SLEUTH

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; CODES (SYMBOLS); DIFFERENTIAL EQUATIONS; EIGENVALUES AND EIGENFUNCTIONS; PROBLEM SOLVING;

SOFTWARE PACKAGE SLEUTH; TWO-POINT FOURTH ORDER STURM-LIOUVILLE EIGENVALUE PROBLEMS;

COMPUTER SOFTWARE;

EID: 0031376840     PISSN: 00983500     EISSN: None     Source Type: Journal    
DOI: 10.1145/279232.279231     Document Type: Article

References (13)

1. BAILEY, P. B., EVERITT, W. N., AND ZETTL, A. 1991. Computing eigenvalues of singluar Sturm-Liouville problems. Results Math. 20, 391-423.
2. 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.
3. GREENBERG, L. 1991a. An oscillation method for fourth-order, self-adjoint, two-point boundary value problems with nonlinear eigenvalues. SIAM J. Math. Anal. 22, 4 (July), 1021-1042.
4. GREENBERG, L. 1991b. A Prüfer method for calculating eigenvalues of self-adjoint systems of ordinary differential equations: Parts 1 and 2. Tech. Rep. TR91-24, University of Maryland at College Park, College Park, MD.
5. GREENBERG, L. AND MARLETTA, M. 1995a. Oscillation theory and numerical solution of fourth order Sturm-Liouville problems. IMA J. Num. Anal. 15, 319-356.
6. GREENBERG, L. AND MARLETTA, M. 1995b. The validity of Richardson extrapolation in coefficient approximation methods for fourth order and higher order self-adjoint ODE eigenvalue problems. Tech. Rep., Department of Mathematics and Computer Science, University of Leicester, Leicester, UK.
7. KRALL, A. M. 1981. Orthogonal polynomials satisfying fourth order differential equations. Proc. Roy. Soc. Edinburgh 87A, 271-288.
8. KWON, K. H., LITTLEJOHN, L. L., LEE, J. K., AND YOO, B. H. 1994. Characterization of classical type orthogonal polynomials. Proc. Am. Math. Soc. 120, 2, 485-493.
9. MARLETTA, M. AND PRYCE, J. D. 1992. Automatic solution of Sturm-Liouville problems using the Pruess method. J. Comput. Appl. Math. 39, 1 (Feb. 28), 57-78.
10. PRUESS, S. AND FULTON, C. T. 1993. Mathematical software for Sturm-Liouville problems. ACM Trans. Math. Softw. 19, 3 (Sept.), 360-376.
11. PRYCE, J. D. 1986. Error control of phase-function shooting methods for Sturm-Liouville problems. IMA J. Num. Anal. 6, 103-123.
12. PRYCE, J. D. 1994. Numerical Solution of Sturm-Liouville Problems. Oxford University Press, Oxford, UK.
13. ROSEAU, M. 1987. Vibrations in Mechanical Systems. Springer-Verlag, Berlin, Germany.