{"id":"https://openalex.org/W2618966431","doi":"https://doi.org/10.1007/s10208-017-9352-1","title":"Low Regularity Exponential-Type Integrators for Semilinear Schr\u00f6dinger Equations","display_name":"Low Regularity Exponential-Type Integrators for Semilinear Schr\u00f6dinger Equations","publication_year":2017,"publication_date":"2017-05-26","ids":{"openalex":"https://openalex.org/W2618966431","doi":"https://doi.org/10.1007/s10208-017-9352-1","mag":"2618966431"},"language":"en","primary_location":{"id":"doi:10.1007/s10208-017-9352-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-017-9352-1","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs10208-017-9352-1.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007%2Fs10208-017-9352-1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047834422","display_name":"Alexander Ostermann","orcid":"https://orcid.org/0000-0003-0194-2481"},"institutions":[{"id":"https://openalex.org/I190249584","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659","country_code":"AT","type":"education","lineage":["https://openalex.org/I190249584"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Alexander Ostermann","raw_affiliation_strings":["Department of Mathematics, University of Innsbruck, Technikerstr.\u00a013, 6020, Innsbruck, Austria"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Innsbruck, Technikerstr.\u00a013, 6020, Innsbruck, Austria","institution_ids":["https://openalex.org/I190249584"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027189972","display_name":"Katharina Schratz","orcid":null},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Katharina Schratz","raw_affiliation_strings":["Fakult\u00e4t f\u00fcr Mathematik, Karlsruhe Institute of Technology, Englerstr.\u00a02, 76131, Karlsruhe, Germany"],"affiliations":[{"raw_affiliation_string":"Fakult\u00e4t f\u00fcr Mathematik, Karlsruhe Institute of Technology, Englerstr.\u00a02, 76131, Karlsruhe, Germany","institution_ids":["https://openalex.org/I102335020"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5047834422"],"corresponding_institution_ids":["https://openalex.org/I190249584"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":7.8142,"has_fulltext":true,"cited_by_count":96,"citation_normalized_percentile":{"value":0.98323353,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"18","issue":"3","first_page":"731","last_page":"755"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9995999932289124,"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":0.9995999932289124,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9872999787330627,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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":0.8626449108123779},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.683324933052063},{"id":"https://openalex.org/keywords/exponential-integrator","display_name":"Exponential integrator","score":0.6189394593238831},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6078664064407349},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5905135869979858},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5621722936630249},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5571008920669556},{"id":"https://openalex.org/keywords/integrator","display_name":"Integrator","score":0.5490772724151611},{"id":"https://openalex.org/keywords/exponential-type","display_name":"Exponential type","score":0.5085114240646362},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.48535171151161194},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43890804052352905},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.42364081740379333},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.18248441815376282},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.1396627128124237},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06407725811004639},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06372818350791931}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8626449108123779},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.683324933052063},{"id":"https://openalex.org/C122700484","wikidata":"https://www.wikidata.org/wiki/Q16148845","display_name":"Exponential integrator","level":5,"score":0.6189394593238831},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6078664064407349},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5905135869979858},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5621722936630249},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5571008920669556},{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.5490772724151611},{"id":"https://openalex.org/C103642545","wikidata":"https://www.wikidata.org/wiki/Q5421531","display_name":"Exponential type","level":2,"score":0.5085114240646362},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.48535171151161194},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43890804052352905},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.42364081740379333},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.18248441815376282},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.1396627128124237},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06407725811004639},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06372818350791931},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10208-017-9352-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-017-9352-1","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs10208-017-9352-1.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:diglib.uibk.ac.at/:4590721","is_oa":true,"landing_page_url":"https://resolver.obvsg.at/urn:nbn:at:at-ubi:3-7154","pdf_url":null,"source":{"id":"https://openalex.org/S4306401999","display_name":"Digital Library of the University of Innsbruck (University of Innsbruck)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I143397708","host_organization_name":"Innsbruck Medical University","host_organization_lineage":["https://openalex.org/I143397708"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1007/s10208-017-9352-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-017-9352-1","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs10208-017-9352-1.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3587333238","display_name":null,"funder_award_id":"CRC 1173","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5106512922","display_name":null,"funder_award_id":"Deutsche Forschungsgemeinschaft (DFG","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6024419964","display_name":null,"funder_award_id":"Deutsche Forschungsgemeinschaft (DFG)","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6052429835","display_name":null,"funder_award_id":"(DFG)","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320326164","display_name":"Medizinische Universit\u00e4t Innsbruck","ror":"https://ror.org/03pt86f80"},{"id":"https://openalex.org/F4320327491","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2618966431.pdf","grobid_xml":"https://content.openalex.org/works/W2618966431.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W1487887263","https://openalex.org/W1544770838","https://openalex.org/W1547431580","https://openalex.org/W1552792047","https://openalex.org/W1816756658","https://openalex.org/W1966991416","https://openalex.org/W1982778586","https://openalex.org/W2005061077","https://openalex.org/W2010640399","https://openalex.org/W2012220122","https://openalex.org/W2022032070","https://openalex.org/W2027319347","https://openalex.org/W2027319740","https://openalex.org/W2035093985","https://openalex.org/W2041905900","https://openalex.org/W2051219688","https://openalex.org/W2059162809","https://openalex.org/W2063814247","https://openalex.org/W2074531708","https://openalex.org/W2089752155","https://openalex.org/W2092400970","https://openalex.org/W2117988589","https://openalex.org/W2125279937","https://openalex.org/W2136491192","https://openalex.org/W2183692121","https://openalex.org/W2275278987","https://openalex.org/W2310212366","https://openalex.org/W2387639988","https://openalex.org/W2947056241","https://openalex.org/W2969232873","https://openalex.org/W3144234811","https://openalex.org/W3209416867","https://openalex.org/W4211077197","https://openalex.org/W4245463005","https://openalex.org/W4255754126","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2993671323","https://openalex.org/W2913079245","https://openalex.org/W2288899673","https://openalex.org/W4300407647","https://openalex.org/W2046360005","https://openalex.org/W2794088623","https://openalex.org/W3038568830","https://openalex.org/W2530543162","https://openalex.org/W3025504071","https://openalex.org/W3042136779"],"abstract_inverted_index":{"We":[0],"introduce":[1],"low":[2,97],"regularity":[3,51,98],"exponential-type":[4,94],"integrators":[5,95],"for":[6,10,34,57,60,96],"nonlinear":[7],"Schr\u00f6dinger":[8,70],"equations":[9],"which":[11],"first-order":[12,30,76],"convergence":[13,31,77],"only":[14],"requires":[15],"the":[16,23,44,54,86,91],"boundedness":[17],"of":[18,22,43,81,90],"one":[19],"additional":[20],"derivative":[21],"solution.":[24],"More":[25],"precisely,":[26],"we":[27,72],"will":[28],"prove":[29,75],"in":[32,36],"$$H^r$$":[33],"solutions":[35,99],"$$H^{r+1}$$":[37],"(with":[38],"$$r":[39],">":[40],"d/2$$":[41],")":[42],"derived":[45],"schemes.":[46,66,107],"This":[47],"allows":[48],"us":[49],"lower":[50],"assumptions":[52],"on":[53],"data":[55],"than":[56],"instance":[58],"required":[59],"classical":[61,102],"splitting":[62,103],"or":[63],"exponential":[64,105],"integration":[65,106],"For":[67],"one-dimensional":[68],"quadratic":[69],"equations,":[71],"can":[73],"even":[74],"without":[78],"any":[79],"loss":[80],"regularity.":[82],"Numerical":[83],"experiments":[84],"underline":[85],"favorable":[87],"error":[88],"behavior":[89],"newly":[92],"introduced":[93],"compared":[100],"to":[101],"and":[104]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":15},{"year":2024,"cited_by_count":12},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":21},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":2}],"updated_date":"2026-03-25T14:56:36.534964","created_date":"2025-10-10T00:00:00"}