{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,6]],"date-time":"2024-09-06T22:06:19Z","timestamp":1725660379608},"publisher-location":"Berlin, Heidelberg","reference-count":10,"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_16","type":"book-chapter","created":{"date-parts":[[2012,2,15]],"date-time":"2012-02-15T14:58:14Z","timestamp":1329317894000},"page":"157-167","source":"Crossref","is-referenced-by-count":5,"title":["An Interval Finite Difference Method of Crank-Nicolson Type for Solving the One-Dimensional Heat Conduction Equation with Mixed Boundary Conditions"],"prefix":"10.1007","author":[{"given":"Malgorzata A.","family":"Jankowska","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"16_CR1","unstructured":"Jankowska, M.A., Marciniak, A.: An Interval Finite Difference Method for Solving the One-Dimensional Heat Equation. LNCS (accepted)"},{"key":"16_CR2","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"},{"issue":"11","key":"16_CR3","first-page":"1604","volume":"4","author":"S. Manikonda","year":"2005","unstructured":"Manikonda, S., Berz, M., Makino, K.: High-order verified solutions of the 3D Laplace equation. WSEAS Transactions on Computers\u00a04(11), 1604\u20131610 (2005)","journal-title":"WSEAS Transactions on Computers"},{"key":"16_CR4","first-page":"49","volume":"24","author":"A. Marciniak","year":"2008","unstructured":"Marciniak, A.: An Interval Difference Method for Solving the Poisson Equation - the First Approach. Pro Dialog\u00a024, 49\u201361 (2008)","journal-title":"Pro Dialog"},{"key":"16_CR5","series-title":"LNCS","first-page":"120","volume-title":"PARA 2010, Part II","author":"A. Marciniak","year":"2012","unstructured":"Marciniak, A.: An Interval Version of the Crank-Nicolson Method \u2013 The First Approach. In: J\u00f3nasson, K. (ed.) PARA 2010, Part II. LNCS, vol.\u00a07134, pp. 120\u2013126. Springer, Heidelberg (2012)"},{"key":"16_CR6","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898717716","volume-title":"Introduction to Interval Analysis","author":"R.E. Moore","year":"2009","unstructured":"Moore, R.E., Kearfott, R.B., Cloud, M.J.: Introduction to Interval Analysis. SIAM, Philadelphia (2009)"},{"issue":"2","key":"16_CR7","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(2), 445\u2013451 (2007)","journal-title":"Journal of Computational and Applied Mathematics"},{"issue":"3-4","key":"16_CR8","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1081\/NFA-100105107","volume":"22","author":"M.T. Nakao","year":"2001","unstructured":"Nakao, M.T.: Numerical verification methods for solutions of ordinary and partial differential equations. Numerical Functional Analysis and Optimization\u00a022(3-4), 321\u2013356 (2001)","journal-title":"Numerical Functional Analysis and Optimization"},{"key":"16_CR9","unstructured":"Smith, G.D.: Numerical Solution of Partial Differential Equations: Finite Difference Methods. Oxford University Press (1995)"},{"issue":"3","key":"16_CR10","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1023\/A:1009976505460","volume":"5","author":"Y. Watanabe","year":"1999","unstructured":"Watanabe, Y., Yamamoto, N., Nakao, M.T.: A Numerical Verification Method of Solutions for the Navier-Stokes Equations. Reliable Computing\u00a05(3), 347\u2013357 (1999)","journal-title":"Reliable Computing"}],"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_16","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,27]],"date-time":"2019-04-27T17:31:39Z","timestamp":1556386299000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-28145-7_16"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012]]},"ISBN":["9783642281440","9783642281457"],"references-count":10,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-28145-7_16","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2012]]}}}