{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T11:59:31Z","timestamp":1770897571847,"version":"3.50.1"},"reference-count":25,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Model. Simul. Sci. Comput."],"published-print":{"date-parts":[[2023,6]]},"abstract":"<jats:p>In this paper, we define a splitting scheme for the N-level Bloch model which makes use of exact numerical solutions of sub-equations. These exact solutions involve matrix exponentials which we want to avoid to calculate at each time-step. The resulting scheme is nonstandard and preserves qualitative properties of the Bloch equations. We explore and compare numerically multiple ways to implement it and in particular take into account the specific structure of the Bloch equations.<\/jats:p>","DOI":"10.1142\/s1793962323500447","type":"journal-article","created":{"date-parts":[[2023,4,14]],"date-time":"2023-04-14T03:18:08Z","timestamp":1681442288000},"source":"Crossref","is-referenced-by-count":3,"title":["Strang splitting schemes for<i>N<\/i>-level Bloch models"],"prefix":"10.1142","volume":"14","author":[{"given":"Marc E.","family":"Songolo","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science, University of Lubumbashi, 1825 Lubumbashi, Republic Democratic of Congo"}]},{"given":"Brigitte","family":"Bid\u00e9garay-Fesquet","sequence":"additional","affiliation":[{"name":"Univ. Grenoble Alpes, CNRS, Grenoble INP\u2020, LJK, 38000 Grenoble, France"}]}],"member":"219","published-online":{"date-parts":[[2023,5,17]]},"reference":[{"issue":"20","key":"S1793962323500447BIB001","doi-asserted-by":"crossref","first-page":"4530","DOI":"10.1109\/JLT.2009.2024627","volume":"27","author":"Andreasen J.","year":"2009","journal-title":"J. Lightwave Technol."},{"issue":"3","key":"S1793962323500447BIB002","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1016\/S0378-4754(02)00106-4","volume":"61","author":"Anguelov R.","year":"2003","journal-title":"Math. Comput. Simul."},{"issue":"3","key":"S1793962323500447BIB003","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1002\/num.10046","volume":"19","author":"Bid\u00e9garay B.","year":"2003","journal-title":"Numer. Methods Part. Differ. Equ."},{"key":"S1793962323500447BIB004","series-title":"Math\u00e9matiques et Applications","doi-asserted-by":"crossref","DOI":"10.1007\/3-540-37725-5","volume-title":"Hi\u00e9rarchie de mod\u00e8les en optique quantique. De Maxwell\u2013Bloch \u00e0 Schr\u00f6dinger non-lin\u00e9aire","volume":"49","author":"Bid\u00e9garay-Fesquet B.","year":"2006"},{"issue":"2","key":"S1793962323500447BIB005","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1006\/jcph.2001.6752","volume":"170","author":"Bid\u00e9garay B.","year":"2001","journal-title":"J. Comput. Phys."},{"key":"S1793962323500447BIB006","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-20561-3","volume-title":"Density Matrix Theory and Applications","author":"Blum K.","year":"2012","edition":"3"},{"key":"S1793962323500447BIB007","volume-title":"Nonlinear Optics","author":"Boyd R. W.","year":"2008","edition":"3"},{"key":"S1793962323500447BIB008","series-title":"CNRS","doi-asserted-by":"crossref","DOI":"10.1051\/978-2-7598-0291-3","volume-title":"Processus d\u2019interaction entre photons et atomes","author":"Cohen-Tannoudji C.","year":"1996"},{"issue":"1","key":"S1793962323500447BIB009","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/j.physd.2003.06.001","volume":"188","author":"Colin T.","year":"2004","journal-title":"Physica D"},{"issue":"3","key":"S1793962323500447BIB010","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1007\/s10013-017-0249-8","volume":"46","author":"Dang Q. A.","year":"2018","journal-title":"Vietnam J. Math."},{"issue":"1","key":"S1793962323500447BIB011","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1007\/s00233-006-0640-3","volume":"74","author":"Farago I.","year":"2007","journal-title":"Semigr. Forum"},{"issue":"7","key":"S1793962323500447BIB012","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1364\/OL.28.000573","volume":"28","author":"Gruetzmacher J. A.","year":"2003","journal-title":"Opt. Lett."},{"key":"S1793962323500447BIB013","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198501770.001.0001","volume-title":"The Quantum Theory of Light","author":"Loudon R.","year":"2000","edition":"3"},{"key":"S1793962323500447BIB014","volume-title":"Nonstandard Finite Difference Models of Differential Equations","author":"Mickens R. E.","year":"1994"},{"key":"S1793962323500447BIB015","doi-asserted-by":"publisher","DOI":"10.1142\/9789812813251_0001"},{"key":"S1793962323500447BIB016","doi-asserted-by":"publisher","DOI":"10.1142\/9789812703316_0001"},{"issue":"1","key":"S1793962323500447BIB017","first-page":"3","volume":"45","author":"Moler C.","year":"2003","journal-title":"SIAM J. Appl. Math."},{"issue":"3","key":"S1793962323500447BIB018","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1109\/8.662652","volume":"46","author":"Nagra A. S.","year":"1998","journal-title":"Trans. Antennas Propag."},{"issue":"4","key":"S1793962323500447BIB020","doi-asserted-by":"crossref","first-page":"1850033:1","DOI":"10.1142\/S1793962318500332","volume":"9","author":"Songolo M. E.","year":"2018","journal-title":"Int. J. Model. Simul. Sci. Comput."},{"issue":"1","key":"S1793962323500447BIB021","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1006\/jcph.2000.6495","volume":"161","author":"Sportisse B.","year":"2000","journal-title":"J. Comput. Phys."},{"issue":"3","key":"S1793962323500447BIB022","doi-asserted-by":"crossref","first-page":"506","DOI":"10.1137\/0705041","volume":"5","author":"Strang G.","year":"1968","journal-title":"SIAM J. Numer. Anal."},{"key":"S1793962323500447BIB024","doi-asserted-by":"crossref","DOI":"10.1002\/9783527617883","volume-title":"Light\u2013Matter Interaction, Fundamentals and Applications","author":"Weiner J.","year":"2003"},{"issue":"4","key":"S1793962323500447BIB025","doi-asserted-by":"crossref","first-page":"3082","DOI":"10.1103\/PhysRevA.52.3082","volume":"53","author":"Ziolkowski R. W.","year":"1995","journal-title":"Phys. Rev. A"},{"issue":"33","key":"S1793962323500447BIB026","doi-asserted-by":"crossref","first-page":"8547","DOI":"10.1364\/AO.36.008547","volume":"36","author":"Ziolkowski R. W.","year":"1997","journal-title":"Appl. Opt."},{"issue":"3","key":"S1793962323500447BIB027","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1109\/8.558653","volume":"45","author":"Ziolkowski R. W.","year":"1997","journal-title":"IEEE Trans. Antennas Propag."}],"container-title":["International Journal of Modeling, Simulation, and Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793962323500447","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,10]],"date-time":"2023-12-10T17:43:08Z","timestamp":1702230188000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S1793962323500447"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,17]]},"references-count":25,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2023,6]]}},"alternative-id":["10.1142\/S1793962323500447"],"URL":"https:\/\/doi.org\/10.1142\/s1793962323500447","relation":{},"ISSN":["1793-9623","1793-9615"],"issn-type":[{"value":"1793-9623","type":"print"},{"value":"1793-9615","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5,17]]},"article-number":"2350044"}}