{"id":"https://openalex.org/W3090624846","doi":"https://doi.org/10.1137/20m1371506","title":"A General Framework of Low Regularity Integrators","display_name":"A General Framework of Low Regularity Integrators","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3090624846","doi":"https://doi.org/10.1137/20m1371506","mag":"3090624846"},"language":"en","primary_location":{"id":"doi:10.1137/20m1371506","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1371506","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2010.01640","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003705634","display_name":"Fr\u00e9d\u00e9ric Rousset","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Fr\u00e9d\u00e9ric Rousset","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5027189972","display_name":"Katharina Schratz","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Katharina Schratz","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5003705634"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9359,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.69555506,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"59","issue":"3","first_page":"1735","last_page":"1768"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9991999864578247,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9909999966621399,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/discretization","display_name":"Discretization","score":0.7008040547370911},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6468944549560547},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6389344930648804},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4914661645889282},{"id":"https://openalex.org/keywords/formalism","display_name":"Formalism (music)","score":0.4910755157470703},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.47859594225883484},{"id":"https://openalex.org/keywords/schr\u00f6dinger-equation","display_name":"Schr\u00f6dinger equation","score":0.44099533557891846},{"id":"https://openalex.org/keywords/wave-equation","display_name":"Wave equation","score":0.4206107556819916},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4171103239059448},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.413494735956192},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16262701153755188}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7008040547370911},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6468944549560547},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6389344930648804},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4914661645889282},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.4910755157470703},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.47859594225883484},{"id":"https://openalex.org/C63036615","wikidata":"https://www.wikidata.org/wiki/Q165498","display_name":"Schr\u00f6dinger equation","level":2,"score":0.44099533557891846},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.4206107556819916},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4171103239059448},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.413494735956192},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16262701153755188},{"id":"https://openalex.org/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","level":1,"score":0.0},{"id":"https://openalex.org/C558565934","wikidata":"https://www.wikidata.org/wiki/Q2743","display_name":"Musical","level":2,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","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}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/20m1371506","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1371506","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:arXiv.org:2010.01640","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2010.01640","pdf_url":"https://arxiv.org/pdf/2010.01640","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:3090624846","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2010.01640","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:HAL:hal-03844934v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03844934","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Numerical Analysis, 2021, 59 (3), pp.1735-1768. &#x27E8;10.1137/20M1371506&#x27E9;","raw_type":"Journal articles"},{"id":"doi:10.48550/arxiv.2010.01640","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2010.01640","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2010.01640","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2010.01640","pdf_url":"https://arxiv.org/pdf/2010.01640","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5887775741","display_name":null,"funder_award_id":"850941","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"}],"funders":[{"id":"https://openalex.org/F4320338335","display_name":"H2020 European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3090624846.pdf","grobid_xml":"https://content.openalex.org/works/W3090624846.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W166242285","https://openalex.org/W1544770838","https://openalex.org/W1593707948","https://openalex.org/W2005061077","https://openalex.org/W2012220122","https://openalex.org/W2048216020","https://openalex.org/W2084367325","https://openalex.org/W2092400970","https://openalex.org/W2117988589","https://openalex.org/W2136491192","https://openalex.org/W2275278987","https://openalex.org/W2517093759","https://openalex.org/W2618966431","https://openalex.org/W2917808692","https://openalex.org/W2949476605","https://openalex.org/W2964133549","https://openalex.org/W2964830467","https://openalex.org/W2968362487","https://openalex.org/W2980497369","https://openalex.org/W3023795180","https://openalex.org/W3024388893","https://openalex.org/W3029245030","https://openalex.org/W3039811077","https://openalex.org/W3092549130","https://openalex.org/W3102415465","https://openalex.org/W3209416867","https://openalex.org/W4211077197","https://openalex.org/W4245463005"],"related_works":["https://openalex.org/W2156404745","https://openalex.org/W3169927171","https://openalex.org/W3086471169","https://openalex.org/W2749737838","https://openalex.org/W2963211427","https://openalex.org/W1538588718","https://openalex.org/W3126639688","https://openalex.org/W3176936211","https://openalex.org/W2793387262","https://openalex.org/W3103163818","https://openalex.org/W2964013139","https://openalex.org/W2963243433","https://openalex.org/W1988206114","https://openalex.org/W2188057694","https://openalex.org/W2912163380","https://openalex.org/W1885159586","https://openalex.org/W2701655469","https://openalex.org/W1977344101","https://openalex.org/W2463439411","https://openalex.org/W2607405612"],"abstract_inverted_index":{"We":[0,131],"introduce":[1],"a":[2,17,23,45],"new":[3,18,42,54,102,116],"general":[4,134],"framework":[5,43,85],"for":[6,22,67],"the":[7,50,53,68,73,83,110,115,137,146,150,154,158],"approximation":[8],"of":[9,20,26,52,109,140],"evolution":[10],"equations":[11,27],"at":[12],"low":[13],"regularity":[14,30],"and":[15,49,87,90,160],"develop":[16],"class":[19],"schemes":[21,55],"wide":[24],"range":[25],"under":[28],"lower":[29],"assumptions":[31],"than":[32],"classical":[33],"methods":[34],"require.":[35],"In":[36,98],"contrast":[37],"to":[38,71,76,80,91,136],"previous":[39],"works,":[40],"our":[41,101,133],"allows":[44,65],"unified":[46],"practical":[47],"formulation":[48],"construction":[51],"does":[56,104],"not":[57,96,120],"rely":[58],"on":[59],"any":[60],"Fourier":[61],"based":[62],"expansions.":[63],"This":[64],"us":[66],"first":[69],"time":[70,117,138],"overcome":[72],"severe":[74],"restriction":[75],"periodic":[77],"boundary":[78,173],"conditions,":[79],"embed":[81],"in":[82,164],"same":[84],"parabolic":[86],"dispersive":[88],"equations,":[89,162],"handle":[92],"nonlinearities":[93],"that":[94],"are":[95],"polynomial.":[97],"particular,":[99],"as":[100,145],"formalism":[103],"no":[105],"longer":[106],"require":[107],"periodicity":[108],"problem,":[111],"one":[112],"may":[113],"couple":[114],"discretization":[118,139],"technique":[119],"only":[121],"with":[122,127,171],"spectral":[123],"methods,":[124],"but":[125],"rather":[126],"various":[128,141],"spatial":[129],"discretizations.":[130],"apply":[132],"theory":[135],"concrete":[142],"PDEs,":[143],"such":[144],"nonlinear":[147,151],"heat":[148],"equation,":[149,153,157],"Schr\u00f6dinger":[152],"complex":[155],"Ginzburg--Landau":[156],"half-wave":[159],"Klein--Gordon":[161],"set":[163],"$\\Omega":[165],"\\subset":[166],"\\mathbb{R}^d$,":[167],"$d":[168],"\\leq":[169],"3$,":[170],"suitable":[172],"conditions.":[174]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}
