{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T12:27:55Z","timestamp":1775478475062,"version":"3.50.1"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[1991,3,1]],"date-time":"1991-03-01T00:00:00Z","timestamp":667785600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computing"],"published-print":{"date-parts":[[1991,3]]},"DOI":"10.1007\/bf02239009","type":"journal-article","created":{"date-parts":[[2005,11,14]],"date-time":"2005-11-14T17:15:41Z","timestamp":1131988541000},"page":"19-34","source":"Crossref","is-referenced-by-count":34,"title":["Computer-assisted existence proofs for two-point boundary value problems","Computer-unterst\u00fctzte Existenzbeweise f\u00fcr Zweipunkt-Randwertprobleme"],"prefix":"10.1007","volume":"46","author":[{"given":"M.","family":"Plum","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"BF02239009_CR1","first-page":"142","volume":"233","author":"N. W. Bazley","year":"1966","unstructured":"Bazley, N. W., Fox, D. W.: Comparison operators for lower bounds to eigenvalues. J. Reine Angew. Math.233, 142\u2013149 (1966).","journal-title":"J. Reine Angew. Math."},{"key":"BF02239009_CR2","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-05500-7","volume-title":"The numerical treatment of differential equations","author":"L. Collatz","year":"1960","unstructured":"Collatz, L.: The numerical treatment of differential equations: Springer, Berlin-G\u00f6ttingen-Heidelberg 1960."},{"key":"BF02239009_CR3","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/BF01111276","volume":"86","author":"H. Ehlich","year":"1964","unstructured":"Ehlich, H., Zeller, K.: Schwankung von Polynomen zwischen Gitterpunkten. Math. Z.86, 41\u201344 (1964).","journal-title":"Math. Z."},{"key":"BF02239009_CR4","unstructured":"G\u00e4rtel, U.: Fehlerabsch\u00e4tzungen f\u00fcr vektorwertige Randwertaufgaben zweiter Ordnung, insbesondere f\u00fcr Probleme aus der chemischen Reaktions-Diffusions-Theorie. Doctoral Dissertation, K\u00f6ln 1987."},{"key":"BF02239009_CR5","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1007\/BF02241862","volume":"44","author":"M. G\u00f6hlen","year":"1990","unstructured":"G\u00f6hlen, M., Plum, M., Schr\u00f6der, J.: A programmed algorithm for existence proofs for two-point boundary value problems. Computing44, 91\u2013132 (1990).","journal-title":"Computing"},{"key":"BF02239009_CR6","series-title":"ISNM","first-page":"58","volume-title":"Numerical treatment of eigenvalue problems, vol. 3","author":"F. Goerisch","year":"1984","unstructured":"Goerisch, F., Albrecht, J.: Eine einheitliche Herleitung von Einschlie\u00dfungss\u00e4tzen f\u00fcr Eigenwerte. In: Albrecht, J., Collatz, L., Velte, W. (eds.): Numerical treatment of eigenvalue problems, vol. 3, pp 58\u201388, ISNM 69. Birkh\u00e4user, Basel 1984."},{"key":"BF02239009_CR7","unstructured":"IBM High-Accuracy Arithmetic Subroutine Library (ACRITH). Program description and user's guide, SC 33-6164-02, 3rd Edition (1986)."},{"key":"BF02239009_CR8","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1137\/0718028","volume":"18","author":"G. Kedem","year":"1981","unstructured":"Kedem, G.: A posteriori error bounds for two-point boundary value problems. SIAM J. Numer. Anal.18, 431\u2013448 (1981).","journal-title":"SIAM J. Numer. Anal."},{"key":"BF02239009_CR9","unstructured":"Kulisch, U.: FORTRAN-SC, language reference and user's guide. University of Karlsruhe and IBM Development Laboratory B\u00f6blingen 1987."},{"key":"BF02239009_CR10","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1007\/BF02162168","volume":"10","author":"L. J. Lehmann","year":"1967","unstructured":"Lehmann, L. J.: Fehlerschranken f\u00fcr N\u00e4herungsl\u00f6sungen bei Differentialgleichungen. Numer. Math.10, 261\u2013288 (1967).","journal-title":"Numer. Math."},{"key":"BF02239009_CR11","unstructured":"Lohner, R.: Einschlie\u00dfung der L\u00f6sung gew\u00f6hnlicher Anfangs- und Randwertaufgaben und Anwendungen. Doctoral Dissertation, Karlsruhe 1988."},{"key":"BF02239009_CR12","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1007\/BF00945108","volume":"41","author":"M. Plum","year":"1990","unstructured":"Plum, M.: Eigenvalue inclusions for second-order ordinary differential operators by a numerical homotopy method. J. Appl. Math. Phys. (ZAMP)41, 205\u2013226 (1990).","journal-title":"J. Appl. Math. Phys. (ZAMP)"},{"key":"BF02239009_CR13","unstructured":"Plum, M.: Existence and inclusion for two-point boundary value problems by numerical means. Proceedings of the IMA Conference on Computational Ordinary Differential Equations (London 1989), Oxford University Press, to appear."},{"key":"BF02239009_CR14","unstructured":"Plum, M.: Verified existence and inclusion results for two-point boundary value problems. Proceedings of the International Symposium SCAN-89 (Basel 1989), to appear in: IMACS Annals on Computing and Applied Mathematics."},{"key":"BF02239009_CR15","unstructured":"Plum, M.: ExplicitH 2-estimates and pointwise bounds for solutions of second-order elliptic boundary value problems, to appear in J. Math. Anal. Appl."},{"key":"BF02239009_CR16","unstructured":"Plum, M.: Existence proofs in combination with error bounds for approximate solutions of weakly nonlinear second-order elliptic boundary value problems. ZAMM 71."},{"key":"BF02239009_CR17","volume-title":"Operator inequalities","author":"J. Schr\u00f6der","year":"1980","unstructured":"Schr\u00f6der, J.: Operator inequalities. Academic Press, New York 1980."},{"key":"BF02239009_CR18","unstructured":"Schr\u00f6der, J.: Existence proofs for boundary value problems by numerical algorithms. Report Univ. Cologne 1986."},{"issue":"Suppl.","key":"BF02239009_CR19","first-page":"9","volume":"6","author":"J. Schr\u00f6der","year":"1988","unstructured":"Schr\u00f6der, J.: A method for producing verified results for two-point boundary value problems. Computing [Suppl. 6], 9\u201322 (1988).","journal-title":"Computing"}],"container-title":["Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02239009.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF02239009\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02239009","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,15]],"date-time":"2019-05-15T17:13:02Z","timestamp":1557940382000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF02239009"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,3]]},"references-count":19,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1991,3]]}},"alternative-id":["BF02239009"],"URL":"https:\/\/doi.org\/10.1007\/bf02239009","relation":{},"ISSN":["0010-485X","1436-5057"],"issn-type":[{"value":"0010-485X","type":"print"},{"value":"1436-5057","type":"electronic"}],"subject":[],"published":{"date-parts":[[1991,3]]}}}