{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T00:47:34Z","timestamp":1791852454177,"version":"4.3.4"},"reference-count":21,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>In this paper, we deduce high-order error bounds for exponential operator splitting methods. The employed techniques are specific to linear differential equations of the form $u'(t) = A \\, u(t) + B \\, u(t)$, $t \\geq 0$, involving an unbounded operator A. In particular, evolutionary Schr\u00f6dinger equations with sufficiently regular initial values are included in the analysis.<\/jats:p>","DOI":"10.1137\/060674636","type":"journal-article","created":{"date-parts":[[2008,4,23]],"date-time":"2008-04-23T18:23:16Z","timestamp":1208974996000},"page":"2022-2038","source":"Crossref","is-referenced-by-count":117,"title":["High-Order Exponential Operator Splitting Methods for Time-Dependent Schr\u00f6dinger Equations"],"prefix":"10.1137","volume":"46","author":[{"given":"Mechthild","family":"Thalhammer","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,4,23]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9991(03)00102-5"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142900381497"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(01)00492-7"},{"key":"R4","unstructured":"S. Blanes, F. Casas, and A. Murua,\n                      On the Linear Stability of Splitting Methods\n                      , Numerical Analysis Reports 8\/2006, University of Cambridge, Cambridge, UK, 2006."},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.4173\/mic.2006.2.2"},{"key":"R6","unstructured":"P. Chartier and A. Murua,\n                      Preserving First Integrals and Volume Forms of Additively Split Systems\n                      , INRIA Report RR-6016, Rennes, France, 2006."},{"key":"R7","unstructured":"K.J. Engel and R. Nagel,\n                      One-Parameter Semigroups for Linear Evolution Equations\n                      , Springer, New York, 2000."},{"key":"R8","doi-asserted-by":"crossref","unstructured":"E. Hairer, Ch. Lubich, and G. Wanner,\n                      Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations\n                      , Springer, Berlin, 2002.","DOI":"10.1007\/978-3-662-05018-7"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142902403875"},{"key":"R10","unstructured":"E. Hille and R.S. Phillips,\n                      Functional Analysis and Semi-Groups\n                      , AMS, Providence, RI, 1957."},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1023\/A:1022396519656"},{"key":"R12","unstructured":"R. Kozlov, A. Kv\u00e6rn\u00f8, and B. Owren,\n                      The Behaviour of the Local Error in Splitting Methods Applied to Stiff Problems\n                      , Preprint Numerics 1\/2003, University of Trondheim, Trondheim, Norway, 2003; also available online from http:\/\/www.math.ntnu.no\/$\\!_{^{\\sim}}\\!$bryn\/trliste.imf (6th report)."},{"key":"R13","unstructured":"R. Kozlov and B. Owren,\n                      Order Reduction in Operator Splitting Methods\n                      , Preprint Numerics 6\/1999, University of Trondheim, Trondheim, Norway, 1999."},{"key":"R14","doi-asserted-by":"crossref","unstructured":"Ch. Lubich,\n                      On Splitting Methods for Schr\u00f6dinger-Poisson and Cubic Nonlinear Schr\u00f6dinger Equations\n                      , preprint, Universit\u00e4t T\u00fcbingen, T\u00fcbingen, Germany, 2007.","DOI":"10.1090\/S0025-5718-08-02101-7"},{"key":"R15","first-page":"5251","volume":"39","author":"McLachlan R.","year":"2006","journal-title":"J. Phys."},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492902000053"},{"key":"R17","doi-asserted-by":"crossref","unstructured":"A. Pazy,\n                      Semigroups of Linear Operators and Applications to Partial Differential Equations\n                      , Springer, New York, 1983.","DOI":"10.1007\/978-1-4612-5561-1"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/14.1.27"},{"key":"R19","unstructured":"B. Sportisse and J.G. Verwer,\n                      A Note on Operator Splitting in the Stiff Linear Case\n                      , Technical report MAS-R9830, CWI Amsterdam, Amsterdam, The Netherlands, 1998."},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1137\/0705041"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1959-0108732-6"}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/060674636","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:14:15Z","timestamp":1787325255000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/060674636"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1]]},"references-count":21,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2008,1]]}},"alternative-id":["10.1137\/060674636"],"URL":"https:\/\/doi.org\/10.1137\/060674636","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,1]]}}}