Automatic Solution of the Sturm-Liouville Problem

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Automatic Solution of the Sturm-Liouville Problem

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 4 , Issue 3 (September 1978) table of contents

Pages: 193 - 208

Year of Publication: 1978

ISSN:0098-3500

Authors

P. B. Bailey	Numerical Mathematics Division 5122, Sandia Laboratories, Albuquerque, NM
M. K. Gordon	Numerical Mathematics Division 5122, Sandia Laboratories, Albuquerque, NM
L. F. Shampine	Numerical Mathematics Division 5122, Sandia Laboratories, Albuquerque, NM

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 6, Downloads (12 Months): 52, Citation Count: 10

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REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	ADAM, G, IXARU, L G, AND CORCIOVEI, A A first-order perturbatlve numerical method for the solution of the radial Schrodmger equation J Comput Phys 22 {1976), 1-33
	2	BAILEY, P B Sturm-Llouvflle elgenvalues vm a phase function. SIAM J. Appl. Math 14 (1966), 242-249
	3	BAmE~', P.B., GORDON, M K, A~D SHAMPINt~, L F Solving Sturm-Llouvflle eigenva\|ue problems Rep SAND76-0560, Sandla Labs, Albuquerque, N Mex, 1976
	4	BERTRAM, L Attenuation of Rayle~gh-Taylor mstablhtles m a Gaussian stratification Private C6mmumcatlon, Sandla Labs, Albuquerque, N Mex
	5	CODDINGTON, E.A. AND LEVINSON, N Theory of Ord,nary D~fferentlal Equations. McGraw- Hill, New York, 1955
	6	COLL, C.F, AND MF.HUS, C.F. Theoretical calculation of Raman scattering cross sections for use in flame analysis. Rep. SAND 76-8204, Sandia Labs., Livermore, Calif. (This report contains a description of the physical problem; the related eigenvalue problem was communicated to the authors privately.)
	7	HARGRAVE, B.A Numerical approximation of elgenvalues of Sturm-Llouville systems. J. Comp. Phys 20 (1976), 381-396.
	8	SCOTT, M.R., SHAMmNE, L.F., AND WING, G.M Invanant imbedding and the calculaUon of eigenvalues for Sturm-Liouville systems Computing 4 (1969), 10-23.
	9	L. F. Shampine , H. A. Watts, Global Error Estimates for Ordinary Differential Equations, ACM Transactions on Mathematical Software (TOMS), v.2 n.2, p.172-186, June 1976 [doi>10.1145/355681.355687]
	10	TITCHMARSH, E.C Ezgenfunctmn Expansmns, Part L Oxford U Press, London, 1962.

CITED BY 10

	Steven Pruess , Charles T. Fulton, Mathematical software for Sturm-Liouville problems, ACM Transactions on Mathematical Software (TOMS), v.19 n.3, p.360-376, Sept. 1993
	Leon Greenberg , Marco Marletta, Algorithm 775: the code SLEUTH for solving fourth-order Sturm-Liouville problems, ACM Transactions on Mathematical Software (TOMS), v.23 n.4, p.453-493, Dec. 1997
	Paul B. Bailey , Anton Zettl, Eigenvalue and eigenfunction computations for Sturm-Liouville problems, ACM Transactions on Mathematical Software (TOMS), v.17 n.4, p.491-499, Dec. 1991
	Hideaki Ishikawa, Numerical methods for the eigenvalue determination of second-order ordinary differential equations, Journal of Computational and Applied Mathematics, v.208 n.2, p.404-424, November, 2007
	V. Ledoux , M. Van Daele , G. Vanden Berghe, MATSLISE: A MATLAB package for the numerical solution of Sturm-Liouville and Schrödinger equations, ACM Transactions on Mathematical Software (TOMS), v.31 n.4, p.532-554, December 2005
	M. Marletta, Eigenvalue problems on exterior domains and Dirichlet to Neumann maps, Journal of Computational and Applied Mathematics, v.171 n.1-2, p.367-391, 1 October 2004
	Michael S. P. Eastham , Charles T. Fulton , Steven Pruess, Using the SLEDGE package on Sturm-Liouville problems having nonempty essential spectra, ACM Transactions on Mathematical Software (TOMS), v.22 n.4, p.423-446, Dec. 1996
	J. D. Pryce, A test package for Sturm-Liouville solvers, ACM Transactions on Mathematical Software (TOMS), v.25 n.1, p.21-57, March 1999
	L. Aceto , P. Ghelardoni , C. Magherini, Boundary Value Methods as an extension of Numerov's method for Sturm--Liouville eigenvalue estimates, Applied Numerical Mathematics, v.59 n.7, p.1644-1656, July, 2009
	P. B. Bailey , W. N. Everitt , A. Zettl, Algorithm 810: The SLEIGN2 Sturm-Liouville Code, ACM Transactions on Mathematical Software (TOMS), v.27 n.2, p.143-192, June 2001