{"id":"https://openalex.org/W3096437315","doi":"https://doi.org/10.1137/20m1378168","title":"Strong Rates of Convergence of a Splitting Scheme for Schr\u00f6dinger Equations with Nonlocal Interaction Cubic Nonlinearity and White Noise Dispersion","display_name":"Strong Rates of Convergence of a Splitting Scheme for Schr\u00f6dinger Equations with Nonlocal Interaction Cubic Nonlinearity and White Noise Dispersion","publication_year":2022,"publication_date":"2022-03-01","ids":{"openalex":"https://openalex.org/W3096437315","doi":"https://doi.org/10.1137/20m1378168","mag":"3096437315"},"language":"en","primary_location":{"id":"doi:10.1137/20m1378168","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1378168","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"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/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-02986230","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025006015","display_name":"Charles-\u00c9douard Br\u00e9hier","orcid":"https://orcid.org/0000-0002-4023-4982"},"institutions":[{"id":"https://openalex.org/I4210104796","display_name":"Institut Camille Jordan","ror":"https://ror.org/01ekw7f87","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I112936343","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I4210104796","https://openalex.org/I4405259976","https://openalex.org/I48430043"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Charles-Edouard Br\u00e9hier","raw_affiliation_strings":["ICJ - Institut Camille Jordan (B\u00e2t. Jean Braconnier 43 bd du 11 novembre 1918 69622 VILLEURBANNE CEDEX - France)","PSPM - Probabilit\u00e9s, statistique, physique math\u00e9matique (France)"],"affiliations":[{"raw_affiliation_string":"ICJ - Institut Camille Jordan (B\u00e2t. Jean Braconnier 43 bd du 11 novembre 1918 69622 VILLEURBANNE CEDEX - France)","institution_ids":["https://openalex.org/I4210104796"]},{"raw_affiliation_string":"PSPM - Probabilit\u00e9s, statistique, physique math\u00e9matique (France)","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047697581","display_name":"David Cohen","orcid":"https://orcid.org/0000-0001-6490-1957"},"institutions":[{"id":"https://openalex.org/I66862912","display_name":"Chalmers University of Technology","ror":"https://ror.org/040wg7k59","country_code":"SE","type":"education","lineage":["https://openalex.org/I66862912"]},{"id":"https://openalex.org/I881427289","display_name":"University of Gothenburg","ror":"https://ror.org/01tm6cn81","country_code":"SE","type":"education","lineage":["https://openalex.org/I881427289"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"David Cohen","raw_affiliation_strings":["Chalmers - Department of Mathematical Sciences (Chalmers University of Technology and University of Gothenburg,\r\nS-412 96 G\u00a8oteborg, Sweden - Sweden)"],"affiliations":[{"raw_affiliation_string":"Chalmers - Department of Mathematical Sciences (Chalmers University of Technology and University of Gothenburg,\r\nS-412 96 G\u00a8oteborg, Sweden - Sweden)","institution_ids":["https://openalex.org/I66862912","https://openalex.org/I881427289"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5025006015"],"corresponding_institution_ids":["https://openalex.org/I4210104796"],"apc_list":null,"apc_paid":null,"fwci":1.6008,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.78121168,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"10","issue":"1","first_page":"453","last_page":"480"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9986000061035156,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9957000017166138,"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/sobolev-space","display_name":"Sobolev space","score":0.7259177565574646},{"id":"https://openalex.org/keywords/integrator","display_name":"Integrator","score":0.664629340171814},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6517876386642456},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6414787173271179},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.6124595403671265},{"id":"https://openalex.org/keywords/white-noise","display_name":"White noise","score":0.6023368835449219},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5649171471595764},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5080499649047852},{"id":"https://openalex.org/keywords/dispersion","display_name":"Dispersion (optics)","score":0.498798131942749},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.48618024587631226},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46292659640312195},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.41385698318481445},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2699149250984192},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.17473182082176208},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.13899698853492737}],"concepts":[{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.7259177565574646},{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.664629340171814},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6517876386642456},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6414787173271179},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.6124595403671265},{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.6023368835449219},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5649171471595764},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5080499649047852},{"id":"https://openalex.org/C177562468","wikidata":"https://www.wikidata.org/wiki/Q182893","display_name":"Dispersion (optics)","level":2,"score":0.498798131942749},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.48618024587631226},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46292659640312195},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.41385698318481445},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2699149250984192},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.17473182082176208},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.13899698853492737},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/20m1378168","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1378168","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"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/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-02986230v1","is_oa":true,"landing_page_url":"https://hal.science/hal-02986230","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM/ASA Journal on Uncertainty Quantification, 2022, 10 (1), ⟨10.1137/20M1378168⟩","raw_type":"Journal articles"},{"id":"pmh:oai:research.chalmers.se:527570","is_oa":false,"landing_page_url":"https://research.chalmers.se/en/publication/527570","pdf_url":null,"source":{"id":"https://openalex.org/S4306402469","display_name":"Chalmers Research (Chalmers University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66862912","host_organization_name":"Chalmers University of Technology","host_organization_lineage":["https://openalex.org/I66862912"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"pmh:oai:research.chalmers.se:530733","is_oa":false,"landing_page_url":"https://research.chalmers.se/en/publication/451e8a3b-c370-4b05-9d0a-a0939ccb68ac","pdf_url":null,"source":{"id":"https://openalex.org/S4306402469","display_name":"Chalmers Research (Chalmers University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66862912","host_organization_name":"Chalmers University of Technology","host_organization_lineage":["https://openalex.org/I66862912"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"pmh:oai:HAL:hal-02986230v1","is_oa":true,"landing_page_url":"https://hal.science/hal-02986230","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM/ASA Journal on Uncertainty Quantification, 2022, 10 (1), ⟨10.1137/20M1378168⟩","raw_type":"Journal articles"},"sustainable_development_goals":[{"score":0.5099999904632568,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G3061504138","display_name":null,"funder_award_id":"ANR-19-CE40-0016","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G5942721400","display_name":null,"funder_award_id":"2018-04443","funder_id":"https://openalex.org/F4320321033","funder_display_name":"Svenska Forskningsr\u00e5det Formas"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320321033","display_name":"Svenska Forskningsr\u00e5det Formas","ror":"https://ror.org/03pjs1y45"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1972836364","https://openalex.org/W2000287596","https://openalex.org/W2041878949","https://openalex.org/W2050432637","https://openalex.org/W2092400970","https://openalex.org/W2464159415","https://openalex.org/W2500884611","https://openalex.org/W2535767897","https://openalex.org/W2599234101","https://openalex.org/W2899165257","https://openalex.org/W2962871701","https://openalex.org/W2962933285","https://openalex.org/W2999112156","https://openalex.org/W3039764731","https://openalex.org/W3094831883","https://openalex.org/W3156711624","https://openalex.org/W4245463005"],"related_works":["https://openalex.org/W2366352762","https://openalex.org/W2613964090","https://openalex.org/W2081322886","https://openalex.org/W2380425739","https://openalex.org/W2006251942","https://openalex.org/W2349324463","https://openalex.org/W1988313539","https://openalex.org/W2027541371","https://openalex.org/W2364741597","https://openalex.org/W4390737069"],"abstract_inverted_index":{"We":[0,22,45],"analyze":[1],"a":[2,56],"splitting":[3,49],"integrator":[4,27],"for":[5,38,59],"the":[6,10,34,48,52,60,63,71,74],"time":[7,26],"discretization":[8],"of":[9,30,62,73],"Schr\u00f6dinger":[11],"equation":[12],"with":[13],"nonlocal":[14],"interaction":[15],"cubic":[16],"nonlinearity":[17],"and":[18],"white":[19],"noise":[20],"dispersion.":[21],"prove":[23,46],"that":[24,47],"this":[25],"has":[28],"order":[29],"convergence":[31,65],"one":[32],"in":[33,41],"$p$th":[35],"mean":[36],"sense,":[37],"any":[39],"$p\\geq1$":[40],"some":[42],"Sobolev":[43],"spaces.":[44],"schemes":[50],"preserves":[51],"$L^2$-norm,":[53],"which":[54],"is":[55],"crucial":[57],"property":[58],"proof":[61],"strong":[64],"result.":[66],"Finally,":[67],"numerical":[68,76],"experiments":[69],"illustrate":[70],"performance":[72],"proposed":[75],"scheme.":[77]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}