{"id":"https://openalex.org/W1973055673","doi":"https://doi.org/10.1137/s0036142902403875","title":"On Magnus Integrators for Time-Dependent Schr\u00f6dinger Equations","display_name":"On Magnus Integrators for Time-Dependent Schr\u00f6dinger Equations","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W1973055673","doi":"https://doi.org/10.1137/s0036142902403875","mag":"1973055673"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142902403875","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142902403875","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","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5445/ir/1000042062","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013995544","display_name":"Marlis Hochbruck","orcid":"https://orcid.org/0000-0002-5968-0480"},"institutions":[{"id":"https://openalex.org/I44260953","display_name":"Heinrich Heine University D\u00fcsseldorf","ror":"https://ror.org/024z2rq82","country_code":"DE","type":"education","lineage":["https://openalex.org/I44260953"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Marlis Hochbruck","raw_affiliation_strings":["University of Dusseldorf;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Dusseldorf;","institution_ids":["https://openalex.org/I44260953"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065792988","display_name":"Christian Lubich","orcid":"https://orcid.org/0000-0003-0105-4927"},"institutions":[{"id":"https://openalex.org/I8087733","display_name":"University of T\u00fcbingen","ror":"https://ror.org/03a1kwz48","country_code":"DE","type":"education","lineage":["https://openalex.org/I8087733"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Christian Lubich","raw_affiliation_strings":["University of T\u00fcbingen"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of T\u00fcbingen","institution_ids":["https://openalex.org/I8087733"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.2452,"has_fulltext":false,"cited_by_count":115,"citation_normalized_percentile":{"value":0.98279382,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"41","issue":"3","first_page":"945","last_page":"963"},"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":0.9944000244140625,"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":0.9933000206947327,"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/integrator","display_name":"Integrator","score":0.9111451506614685},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7969986200332642},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.674929678440094},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.564633309841156},{"id":"https://openalex.org/keywords/schr\u00f6dinger-equation","display_name":"Schr\u00f6dinger equation","score":0.460400253534317},{"id":"https://openalex.org/keywords/contrast","display_name":"Contrast (vision)","score":0.4490087330341339},{"id":"https://openalex.org/keywords/variational-integrator","display_name":"Variational integrator","score":0.41408947110176086},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3782123625278473},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.1413804590702057},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12148985266685486},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07326799631118774}],"concepts":[{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.9111451506614685},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7969986200332642},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.674929678440094},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.564633309841156},{"id":"https://openalex.org/C63036615","wikidata":"https://www.wikidata.org/wiki/Q165498","display_name":"Schr\u00f6dinger equation","level":2,"score":0.460400253534317},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.4490087330341339},{"id":"https://openalex.org/C52154503","wikidata":"https://www.wikidata.org/wiki/Q7915797","display_name":"Variational integrator","level":4,"score":0.41408947110176086},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3782123625278473},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.1413804590702057},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12148985266685486},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07326799631118774},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/s0036142902403875","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142902403875","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"},{"id":"pmh:oai:EVASTAR-Karlsruhe.de:1000042062","is_oa":false,"landing_page_url":"https://publikationen.bibliothek.kit.edu/1000042062","pdf_url":null,"source":{"id":"https://openalex.org/S4306401992","display_name":"Repository KITopen (Karlsruhe Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I102335020","host_organization_name":"Karlsruhe Institute of Technology","host_organization_lineage":["https://openalex.org/I102335020"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis, 41 (3), 945-963","raw_type":"doc-type:article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.7.3175","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.7.3175","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.uni-tuebingen.de/uni/opx/reports/lubich_179.ps.gz","raw_type":"text"},{"id":"pmh:oai:bibcyt.ucla.edu.ve:T070300013552/7","is_oa":false,"landing_page_url":"http://bibcyt.ucla.edu.ve/cgi-win/be_alex.exe?Acceso=T070300013552/7&Nombrebd=Bciucla","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},{"id":"doi:10.5445/ir/1000042062","is_oa":true,"landing_page_url":"https://doi.org/10.5445/ir/1000042062","pdf_url":null,"source":{"id":"https://openalex.org/S7407052948","display_name":"KITopen","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.5445/ir/1000042062","is_oa":true,"landing_page_url":"https://doi.org/10.5445/ir/1000042062","pdf_url":null,"source":{"id":"https://openalex.org/S7407052948","display_name":"KITopen","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334763","display_name":"Leibniz-Gemeinschaft","ror":"https://ror.org/01n6r0e97"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1560060148","https://openalex.org/W1567419358","https://openalex.org/W1592378316","https://openalex.org/W1608348832","https://openalex.org/W1624156688","https://openalex.org/W2000224173","https://openalex.org/W2001554107","https://openalex.org/W2039763880","https://openalex.org/W2061356302","https://openalex.org/W2062864779","https://openalex.org/W2095261307","https://openalex.org/W2141320665","https://openalex.org/W2167375272"],"related_works":["https://openalex.org/W2537694785","https://openalex.org/W2006096639","https://openalex.org/W2961659155","https://openalex.org/W2005694504","https://openalex.org/W3011672241","https://openalex.org/W1989699225","https://openalex.org/W2029535240","https://openalex.org/W2593289484","https://openalex.org/W4297670989","https://openalex.org/W49167663"],"abstract_inverted_index":{"Numerical":[0],"methods":[1,39],"based":[2],"on":[3,80],"the":[4,38,67,75,85],"Magnus":[5],"expansion":[6],"are":[7,57],"an":[8,23],"efficient":[9],"class":[10],"of":[11,66,84],"integrators":[12],"for":[13,33,43],"Schr\u00f6dinger":[14],"equations":[15],"with":[16],"time-dependent":[17],"Hamiltonian.":[18],"Though":[19],"their":[20],"derivation":[21],"assumes":[22],"unreasonably":[24],"small":[25],"time":[26,82],"step":[27,46,68],"size,":[28],"as":[29],"would":[30],"be":[31],"required":[32],"a":[34],"standard":[35,73],"explicit":[36],"integrator,":[37],"perform":[40],"well":[41],"even":[42],"much":[44],"larger":[45],"sizes.":[47],"This":[48],"favorable":[49],"behavior":[50],"is":[51,88],"explained,":[52],"and":[53],"optimal-order":[54],"error":[55,76],"bounds":[56],"derived":[58],"that":[59],"require":[60],"no":[61],"or":[62],"only":[63],"mild":[64],"restrictions":[65],"size.":[69],"In":[70],"contrast":[71],"to":[72],"integrators,":[74],"does":[77],"not":[78],"depend":[79],"higher":[81],"derivatives":[83],"solution,":[86],"which":[87],"in":[89],"general":[90],"highly":[91],"oscillatory.":[92]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":6}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}