{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,6]],"date-time":"2024-09-06T22:06:16Z","timestamp":1725660376247},"publisher-location":"Berlin, Heidelberg","reference-count":18,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642281440"},{"type":"electronic","value":"9783642281457"}],"license":[{"start":{"date-parts":[[2012,1,1]],"date-time":"2012-01-01T00:00:00Z","timestamp":1325376000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2012]]},"DOI":"10.1007\/978-3-642-28145-7_12","type":"book-chapter","created":{"date-parts":[[2012,2,15]],"date-time":"2012-02-15T19:58:14Z","timestamp":1329335894000},"page":"120-126","source":"Crossref","is-referenced-by-count":4,"title":["An Interval Version of the Crank-Nicolson Method \u2013 The First Approach"],"prefix":"10.1007","author":[{"given":"Andrzej","family":"Marciniak","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"12_CR1","doi-asserted-by":"publisher","first-page":"41","DOI":"10.12921\/cmst.2000.06.01.41-59","volume":"6","author":"K. Gajda","year":"2000","unstructured":"Gajda, K., Marciniak, A., Szyszka, B.: Three- and four-stage implicit interval methods of Runge-Kutta Type. Computational Methods in Science and Technology\u00a06, 41\u201359 (2000)","journal-title":"Computational Methods in Science and Technology"},{"issue":"1","key":"12_CR2","doi-asserted-by":"publisher","first-page":"17","DOI":"10.12921\/cmst.2002.08.01.17-30","volume":"8","author":"M. Jankowska","year":"2002","unstructured":"Jankowska, M., Marciniak, A.: Implicit interval multistep methods for solving the initial value problem. Computational Methods in Science and Technology\u00a08(1), 17\u201330 (2002)","journal-title":"Computational Methods in Science and Technology"},{"issue":"2","key":"12_CR3","doi-asserted-by":"publisher","first-page":"46","DOI":"10.12921\/cmst.2002.08.02.46-57","volume":"8","author":"M. Jankowska","year":"2002","unstructured":"Jankowska, M., Marciniak, A.: On explicit interval methods of Adams-Bashforth type. Computational Methods in Science and Technology\u00a08(2), 46\u201347 (2002)","journal-title":"Computational Methods in Science and Technology"},{"issue":"2","key":"12_CR4","doi-asserted-by":"publisher","first-page":"109","DOI":"10.12921\/cmst.2006.12.02.109-113","volume":"12","author":"M. Jankowska","year":"2006","unstructured":"Jankowska, M., Marciniak, A.: On two families of implicit interval methods of Adams-Moulton type. Computational Methods in Science and Technology\u00a012(2), 109\u2013114 (2006)","journal-title":"Computational Methods in Science and Technology"},{"key":"12_CR5","doi-asserted-by":"publisher","first-page":"53","DOI":"10.12921\/cmst.1999.05.01.53-65","volume":"5","author":"A. Marciniak","year":"1999","unstructured":"Marciniak, A., Szyszka, B.: One- and two-stage implicit interval methods of Runge-Kutta type. Computational Methods in Science and Technology\u00a05, 53\u201365 (1999)","journal-title":"Computational Methods in Science and Technology"},{"key":"12_CR6","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1023\/B:NUMA.0000049471.81341.60","volume":"37","author":"A. Marciniak","year":"2004","unstructured":"Marciniak, A.: Implicit interval methods for solving the initial value problem. Numerical Algorithms\u00a037, 241\u2013251 (2004)","journal-title":"Numerical Algorithms"},{"issue":"1","key":"12_CR7","doi-asserted-by":"publisher","first-page":"23","DOI":"10.12921\/cmst.2007.13.01.23-29","volume":"13","author":"A. Marciniak","year":"2007","unstructured":"Marciniak, A.: Multistep interval methods of Nystr\u00f6m and Milne-Simpson types. Computational Methods in Science and Technology\u00a013(1), 23\u201340 (2007)","journal-title":"Computational Methods in Science and Technology"},{"issue":"2","key":"12_CR8","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1016\/j.cam.2005.07.036","volume":"199","author":"A. Marciniak","year":"2007","unstructured":"Marciniak, A.: On multistep interval methods for solving the initial value problem. Journal of Computational and Applied Mathematics\u00a0199(2), 229\u2013238 (2007)","journal-title":"Journal of Computational and Applied Mathematics"},{"key":"12_CR9","unstructured":"Marciniak, A.: Selected Interval Methods for Solving the Initial Value Problem. Publishing House of Poznan University of Technology (2009)"},{"key":"12_CR10","first-page":"49","volume":"24","author":"A. Marciniak","year":"2008","unstructured":"Marciniak, A.: An interval difference method for solving the Poisson equation \u2013 the first approach. Pro Dialog\u00a024, 49\u201361 (2008)","journal-title":"Pro Dialog"},{"key":"12_CR11","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1016\/0377-0427(91)90179-N","volume":"38","author":"M.T. Nakao","year":"1991","unstructured":"Nakao, M.T.: Solving nonlinear parabolic problems with result verification. Part I: one-space dimensional case. Journal of Computational and Applied Mathematics\u00a038, 323\u2013324 (1991)","journal-title":"Journal of Computational and Applied Mathematics"},{"key":"12_CR12","doi-asserted-by":"publisher","first-page":"543","DOI":"10.1080\/01630569908816910","volume":"20","author":"K. Nagatou","year":"1999","unstructured":"Nagatou, K., Yamamoto, N., Nakao, M.T.: An approach to the numerical verification of solutions for nonlinear elliptic problem with local uniqueness. Numerical Functional Analysis and Optimization\u00a020, 543\u2013565 (1999)","journal-title":"Numerical Functional Analysis and Optimization"},{"key":"12_CR13","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1007\/978-3-7091-6280-4_19","volume-title":"Symbolic Algebraic Methods and Verification Methods","author":"M. Plum","year":"2001","unstructured":"Plum, M.: Safe numerical error bounds for solutions of nonlinear elliptic boundary value problems. In: Alefeld, G., Rohn, J., Rump, S. (eds.) Symbolic Algebraic Methods and Verification Methods, pp. 195\u2013205. Springer, Heidelberg (2001)"},{"key":"12_CR14","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1016\/S0024-3795(00)00273-1","volume":"324","author":"M. Plum","year":"2001","unstructured":"Plum, M.: Computer-assisted enclosure methods for elliptic differential equations. Linear Algebra and its Applications\u00a0324, 147\u2013187 (2001)","journal-title":"Linear Algebra and its Applications"},{"key":"12_CR15","doi-asserted-by":"publisher","first-page":"445","DOI":"10.1016\/j.cam.2005.09.031","volume":"199","author":"K. Nagatou","year":"2007","unstructured":"Nagatou, K., Hashimoto, K., Nakao, M.T.: Numerical verification of stationary solutions for Navier-Stokes problems. Journal of Computational and Applied Mathematics\u00a0199, 445\u2013451 (2007)","journal-title":"Journal of Computational and Applied Mathematics"},{"key":"12_CR16","unstructured":"Smith, G.D.: Numerical Solution of Partial Differential Equations: Finite Difference Methods. Oxford University Press (1995)"},{"key":"12_CR17","doi-asserted-by":"crossref","unstructured":"Lapidus, L., Pinder, G.F.: Numerical Solution of Partial Differential Equations in Science and Engineering. J. Wiley & Sons (1982)","DOI":"10.2307\/2007712"},{"key":"12_CR18","doi-asserted-by":"crossref","unstructured":"Morton, K.W., Mayers, D.F.: Numerical Solution of Partial Differential Equations: An Introduction. Cambridge University Press (2005)","DOI":"10.1017\/CBO9780511812248"}],"container-title":["Lecture Notes in Computer Science","Applied Parallel and Scientific Computing"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-28145-7_12","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,23]],"date-time":"2019-06-23T19:44:30Z","timestamp":1561319070000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-28145-7_12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012]]},"ISBN":["9783642281440","9783642281457"],"references-count":18,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-28145-7_12","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2012]]}}}