{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,3,24]],"date-time":"2023-03-24T01:51:27Z","timestamp":1679622687595},"reference-count":21,"publisher":"Association for Computing Machinery (ACM)","issue":"3","content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Math. Softw."],"published-print":{"date-parts":[[1993,9]]},"abstract":"Software is described for the Sturm-Liouville eigenproblem. Eigenvalues, eigenfunctions, and spectral density functions can be estimated with global error control. The method of approximating the coefficients forms the mathematical basis. The underlying algorithms are briefly described, and several examples are presented.<\/jats:p>","DOI":"10.1145\/155743.155791","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T11:29:03Z","timestamp":1027769343000},"page":"360-376","update-policy":"http:\/\/dx.doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":94,"title":["Mathematical software for Sturm-Liouville problems"],"prefix":"10.1145","volume":"19","author":[{"given":"Steven","family":"Pruess","sequence":"first","affiliation":[{"name":"Colorado School of Mines, Golden"}]},{"given":"Charles T.","family":"Fulton","sequence":"additional","affiliation":[{"name":"Florida Institute of Technology, Melbourne"}]}],"member":"320","published-online":{"date-parts":[[1993,9]]},"reference":[{"key":"e_1_2_1_1_2","doi-asserted-by":"publisher","DOI":"10.1145\/355791.355792"},{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1145\/210232.210239"},{"key":"e_1_2_1_3_2","volume-title":"Ordinary differential equations","author":"BIRK~ OFF","year":"1969","unstructured":"BIRK~ t OFF , G., AND ROTA , G. Ordinary differential equations . Prentice-Hall , Englewood Cliffs, N.J. , 1969 . BIRK~tOFF, G., AND ROTA, G. Ordinary differential equations. Prentice-Hall, Englewood Cliffs, N.J., 1969."},{"key":"e_1_2_1_4_2","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1016\/0022-247X(67)90009-1","article-title":"Asymptotic eigenvalues of Sturm-Liouville systems","volume":"19","year":"1967","unstructured":"Fix, G . Asymptotic eigenvalues of Sturm-Liouville systems . J. Math. Anal. Appl. 19 ( 1967 ), 519 - 525 . Fix, G. Asymptotic eigenvalues of Sturm-Liouville systems. J. Math. Anal. Appl. 19 (1967), 519-525.","journal-title":"J. Math. Anal. Appl."},{"key":"e_1_2_1_5_2","first-page":"293","article-title":"Two-point boundary value problems with eigenvalue parameter contained in the boundary condition. Proc. Roy. Soc. Edinburgh","volume":"77","author":"FULTON C","year":"1977","unstructured":"FULTON , C . Two-point boundary value problems with eigenvalue parameter contained in the boundary condition. Proc. Roy. Soc. Edinburgh , Sect. A , 77 ( 1977 ), 293 - 308 . FULTON, C. Two-point boundary value problems with eigenvalue parameter contained in the boundary condition. Proc. Roy. Soc. Edinburgh, Sect. A, 77 (1977), 293-308.","journal-title":"Sect. A"},{"key":"e_1_2_1_6_2","first-page":"1","article-title":"Singular eigenvalue problems with eigenvalue parameter contained in the boundary condition. Proc. Roy. Soc. Edinburgh","volume":"87","author":"FULTON C","year":"1980","unstructured":"FULTON , C . Singular eigenvalue problems with eigenvalue parameter contained in the boundary condition. Proc. Roy. Soc. Edinburgh , Sect. A , 87 ( 1980 ) 1 - 34 . FULTON, C. Singular eigenvalue problems with eigenvalue parameter contained in the boundary condition. Proc. Roy. Soc. Edinburgh, Sect. A, 87 (1980) 1-34.","journal-title":"Sect. A"},{"key":"e_1_2_1_7_2","unstructured":"FULTON C. AND PRUESS S. Eigenvalue and eigenfunction asymptotics for regular Sturm- Liouville problems. To appear in J. Math. Anal. Appl. FULTON C. AND PRUESS S. Eigenvalue and eigenfunction asymptotics for regular Sturm- Liouville problems. To appear in J. Math. Anal. Appl."},{"key":"e_1_2_1_8_2","first-page":"77","volume-title":"Proceedings of the Focused Research Program on Spectral Theory and Boundary Value Problems. Argonne National Laboratory Mathematical and Computer Sciences Div.","author":"FULTON C.","year":"1989","unstructured":"FULTON , C. , AND PRUESS , S. A user's guide to the subroutine SPDNSF . In Proceedings of the Focused Research Program on Spectral Theory and Boundary Value Problems. Argonne National Laboratory Mathematical and Computer Sciences Div. , 1989 , 77 - 102 . FULTON, C., AND PRUESS, S. A user's guide to the subroutine SPDNSF. In Proceedings of the Focused Research Program on Spectral Theory and Boundary Value Problems. Argonne National Laboratory Mathematical and Computer Sciences Div., 1989, 77-102."},{"key":"e_1_2_1_9_2","volume-title":"Mathematical software for Sturm-Liouville problems. NSF final report","author":"FULTON C.","year":"1989","unstructured":"FULTON , C. , AND PRUESS , S. Mathematical software for Sturm-Liouville problems. NSF final report , 1989 . FULTON, C., AND PRUESS, S. Mathematical software for Sturm-Liouville problems. NSF final report, 1989."},{"key":"e_1_2_1_10_2","unstructured":"FULTON C. PRUESS S. AND XIE V. The automatic classification of Sturm-Liouville problems. Submitted for publication. FULTON C. PRUESS S. AND XIE V. The automatic classification of Sturm-Liouville problems. Submitted for publication."},{"key":"e_1_2_1_11_2","first-page":"253","article-title":"On the determination of a dittbrential equation from its spectral function","author":"GELFAND I.","year":"1955","unstructured":"GELFAND , I. , AND LEV l TAN , B . On the determination of a dittbrential equation from its spectral function . Am. Math. Soc. Transl. I ( 1955 ), 253 - 304 . GELFAND, I., AND LEVlTAN, B. On the determination of a dittbrential equation from its spectral function. Am. Math. Soc. Transl. I (1955), 253-304.","journal-title":"Am. Math. Soc. Transl."},{"key":"e_1_2_1_12_2","first-page":"511","article-title":"Equidistributing meshes with constraints","author":"KAUTSKY J.","year":"1980","unstructured":"KAUTSKY , J. , AND NICHOLS , N . Equidistributing meshes with constraints . SIAM J. Sci. Stat. Comput. I ( 1980 ), 499 511 . KAUTSKY, J., AND NICHOLS, N. Equidistributing meshes with constraints. SIAM J. Sci. Stat. Comput. I (1980), 499 511.","journal-title":"SIAM J. Sci. Stat. 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Estimating the eigenvalues of Sturm-Liouville problems by approximating the differential equation . SIAM J. Numer. Anal. 10 ( 1973 ), 55 - 68 . PRUESS, S. Estimating the eigenvalues of Sturm-Liouville problems by approximating the differential equation. SIAM J. Numer. Anal. 10 (1973), 55-68.","journal-title":"SIAM J. Numer. Anal."},{"key":"e_1_2_1_15_2","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1090\/S0025-5718-1973-0371100-1","article-title":"Solving linear boundary value problems by approximating the coefficients","volume":"27","author":"PRUESS S","year":"1973","unstructured":"PRUESS , S . Solving linear boundary value problems by approximating the coefficients . Math. Comput. 27 ( 1973 ), 551 - 561 . PRUESS, S. Solving linear boundary value problems by approximating the coefficients. Math. Comput. 27 (1973), 551-561.","journal-title":"Math. 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Anal."},{"key":"e_1_2_1_19_2","volume-title":"Preprint","author":"PRYCE J.","year":"1989","unstructured":"PRYCE , J. , AND MARLETTA , M. A new multipurpose software package for Schr5dinger and Sturm-Liouville computations . Preprint , 1989 . PRYCE, J., AND MARLETTA, M. A new multipurpose software package for Schr5dinger and Sturm-Liouville computations. Preprint, 1989."},{"key":"e_1_2_1_20_2","volume-title":"I","author":"TITCHMARSH","year":"1962","unstructured":"TITCHMARSH , E E~genfunction Expansions Associated w~th Second Order D~fferentml Equations , I . 2 nd Ed, Oxford University Press , London , 1962 . TITCHMARSH, E E~genfunction Expansions Associated w~th Second Order D~fferentml Equations, I. 2nd Ed, Oxford University Press, London, 1962.","edition":"2"},{"key":"e_1_2_1_21_2","first-page":"96","article-title":"On a device for computing the e,~(S~) transformation","volume":"10","author":"WYNN P","year":"1956","unstructured":"WYNN , P . On a device for computing the e,~(S~) transformation . Math. Tables Aid Comput. 10 ( 1956 ), 91 96 . WYNN, P. On a device for computing the e,~(S~) transformation. Math. Tables Aid Comput. 10 (1956), 91 96.","journal-title":"Math. 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