{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,6]],"date-time":"2026-06-06T16:12:01Z","timestamp":1780762321231,"version":"3.54.1"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013,4,1]]},"abstract":"<jats:title>Abstract.<\/jats:title><jats:p>\nThis paper presents the analysis of the split step solvers\nfor multidimensional Schr\u00f6dinger problems.\nThe second-order symmetrical splitting\ntechniques are applied. The standard operator splitting is used\nto split the linear diffraction and reaction\/potential processes.\nThe dimension splitting exploits\nthe commuting property of one-dimensional discrete diffraction operators.\nAlternating Direction Implicit (ADI) and Locally One-Dimensional (LOD)\nalgorithms are constructed and stability is investigated for\ntwo- and three-dimensional problems. Compact\nhigh-order approximations are applied to discretize diffraction operators.\nResults of numerical experiments are presented and convergence\nof finite difference schemes is investigated.\n<\/jats:p>","DOI":"10.1515\/cmam-2013-0004","type":"journal-article","created":{"date-parts":[[2013,9,27]],"date-time":"2013-09-27T16:01:19Z","timestamp":1380297679000},"page":"237-250","source":"Crossref","is-referenced-by-count":14,"title":["Comparison of Split Step Solvers for Multidimensional Schr\u00f6dinger Problems"],"prefix":"10.1515","volume":"13","author":[{"given":"Raimondas","family":"\u010ciegis","sequence":"first","affiliation":[{"name":"1Vilnius Gediminas Technical University, Saul\u0117tekio al.\u00a011, 10223 Vilnius, Lithuania"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Aleksas","family":"Mirinavi\u010dius","sequence":"additional","affiliation":[{"name":"2Vilnius Gediminas Technical University, Saul\u0117tekio al.\u00a011, 10223 Vilnius, Lithuania"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mindaugas","family":"Radziunas","sequence":"additional","affiliation":[{"name":"3Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr.\u00a039, 10117 Berlin, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"374","container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/13\/2\/article-p237.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/downloadpdf\/journals\/cmam\/13\/2\/article-p237.xml","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,28]],"date-time":"2021-02-28T03:03:40Z","timestamp":1614481420000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2013-0004\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,4,1]]},"references-count":0,"journal-issue":{"issue":"2"},"URL":"https:\/\/doi.org\/10.1515\/cmam-2013-0004","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"value":"1609-4840","type":"print"},{"value":"1609-9389","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,4,1]]}}}