{"id":"https://openalex.org/W2051494558","doi":"https://doi.org/10.1137/060674636","title":"High-Order Exponential Operator Splitting Methods for Time-Dependent Schr\u00f6dinger Equations","display_name":"High-Order Exponential Operator Splitting Methods for Time-Dependent Schr\u00f6dinger Equations","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2051494558","doi":"https://doi.org/10.1137/060674636","mag":"2051494558"},"language":"en","primary_location":{"id":"doi:10.1137/060674636","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060674636","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111586019","display_name":"Mechthild Thalhammer","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Mechthild Thalhammer","raw_affiliation_strings":["Mechthild.Thalhammer@uibk.ac.at#TAB#"],"affiliations":[{"raw_affiliation_string":"Mechthild.Thalhammer@uibk.ac.at#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5111586019"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.7316,"has_fulltext":false,"cited_by_count":122,"citation_normalized_percentile":{"value":0.97503404,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"46","issue":"4","first_page":"2022","last_page":"2038"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8595374822616577},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.6806085109710693},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5715517401695251},{"id":"https://openalex.org/keywords/operator-splitting","display_name":"Operator splitting","score":0.5040761232376099},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.46591877937316895},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42966726422309875},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4187551736831665},{"id":"https://openalex.org/keywords/schr\u00f6dinger-equation","display_name":"Schr\u00f6dinger equation","score":0.4108472466468811}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8595374822616577},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.6806085109710693},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5715517401695251},{"id":"https://openalex.org/C2987355758","wikidata":"https://www.wikidata.org/wiki/Q25037251","display_name":"Operator splitting","level":2,"score":0.5040761232376099},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.46591877937316895},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42966726422309875},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4187551736831665},{"id":"https://openalex.org/C63036615","wikidata":"https://www.wikidata.org/wiki/Q165498","display_name":"Schr\u00f6dinger equation","level":2,"score":0.4108472466468811},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/060674636","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060674636","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1492498476","https://openalex.org/W1527296550","https://openalex.org/W1544770838","https://openalex.org/W1592378316","https://openalex.org/W1606157354","https://openalex.org/W1973055673","https://openalex.org/W1997126380","https://openalex.org/W2012220122","https://openalex.org/W2049161806","https://openalex.org/W2070087054","https://openalex.org/W2079477617","https://openalex.org/W2082199698","https://openalex.org/W2083561837","https://openalex.org/W2155509452","https://openalex.org/W2155579513","https://openalex.org/W2947056241","https://openalex.org/W4245463005"],"related_works":["https://openalex.org/W2318982644","https://openalex.org/W2290544825","https://openalex.org/W1929059506","https://openalex.org/W2015183833","https://openalex.org/W24076686","https://openalex.org/W4302343375","https://openalex.org/W2998440535","https://openalex.org/W2151666513","https://openalex.org/W412354254","https://openalex.org/W4379522615"],"abstract_inverted_index":{"In":[0,42],"this":[1],"paper,":[2],"we":[3],"deduce":[4],"high-order":[5],"error":[6],"bounds":[7],"for":[8],"exponential":[9],"operator":[10,40],"splitting":[11],"methods.":[12],"The":[13],"employed":[14],"techniques":[15],"are":[16,52],"specific":[17],"to":[18],"linear":[19],"differential":[20],"equations":[21,46],"of":[22],"the":[23,55],"form":[24],"$u'(t)":[25],"=":[26],"A":[27],"\\,":[28,32],"u(t)":[29],"+":[30],"B":[31],"u(t)$,":[33],"$t":[34],"\\geq":[35],"0$,":[36],"involving":[37],"an":[38],"unbounded":[39],"A.":[41],"particular,":[43],"evolutionary":[44],"Schr\u00f6dinger":[45],"with":[47],"sufficiently":[48],"regular":[49],"initial":[50],"values":[51],"included":[53],"in":[54],"analysis.":[56]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":13},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":11}],"updated_date":"2026-03-17T09:09:15.849793","created_date":"2025-10-10T00:00:00"}