{"id":"https://openalex.org/W2795033786","doi":"https://doi.org/10.1137/18m1177445","title":"Error Estimates of a Regularized Finite Difference Method for the Logarithmic Schr\u00f6dinger Equation","display_name":"Error Estimates of a Regularized Finite Difference Method for the Logarithmic Schr\u00f6dinger Equation","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2795033786","doi":"https://doi.org/10.1137/18m1177445","mag":"2795033786"},"language":"en","primary_location":{"id":"doi:10.1137/18m1177445","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1177445","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1803.10068","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Weizhu Bao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Weizhu Bao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"R\u00e9mi Carles","orcid":"https://orcid.org/0000-0002-3697-2026"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"R\u00e9mi Carles","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-3697-2026","affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Chunmei Su","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chunmei Su","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Qinglin Tang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Qinglin Tang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.3257,"has_fulltext":true,"cited_by_count":49,"citation_normalized_percentile":{"value":0.98777506,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"57","issue":"2","first_page":"657","last_page":"680"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.413100004196167,"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"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.413100004196167,"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/T11416","display_name":"Numerical methods for differential equations","score":0.188400000333786,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.06639999896287918,"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/logarithm","display_name":"Logarithm","score":0.7243000268936157},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7063999772071838},{"id":"https://openalex.org/keywords/discretization-error","display_name":"Discretization error","score":0.6597999930381775},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.6431999802589417},{"id":"https://openalex.org/keywords/round-off-error","display_name":"Round-off error","score":0.6057999730110168},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.5741000175476074},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.51910001039505},{"id":"https://openalex.org/keywords/error-analysis","display_name":"Error analysis","score":0.48080000281333923},{"id":"https://openalex.org/keywords/approximation-error","display_name":"Approximation error","score":0.4433000087738037}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8446999788284302},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.7243000268936157},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7063999772071838},{"id":"https://openalex.org/C126148662","wikidata":"https://www.wikidata.org/wiki/Q3890355","display_name":"Discretization error","level":3,"score":0.6597999930381775},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.6431999802589417},{"id":"https://openalex.org/C61005703","wikidata":"https://www.wikidata.org/wiki/Q2145211","display_name":"Round-off error","level":2,"score":0.6057999730110168},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.5741000175476074},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5687000155448914},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.51910001039505},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.48080000281333923},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.4433000087738037},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.427700012922287},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.42579999566078186},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.39719998836517334},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.39559999108314514},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.3580000102519989},{"id":"https://openalex.org/C202286095","wikidata":"https://www.wikidata.org/wiki/Q579262","display_name":"Error function","level":2,"score":0.34619998931884766},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3366999924182892},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.31929999589920044},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.3174999952316284},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.31630000472068787},{"id":"https://openalex.org/C103088060","wikidata":"https://www.wikidata.org/wiki/Q1062839","display_name":"Error detection and correction","level":2,"score":0.31540000438690186},{"id":"https://openalex.org/C104942944","wikidata":"https://www.wikidata.org/wiki/Q3434686","display_name":"Truncation error","level":2,"score":0.2930999994277954},{"id":"https://openalex.org/C108268861","wikidata":"https://www.wikidata.org/wiki/Q1747602","display_name":"Finite difference coefficient","level":4,"score":0.28839999437332153},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.2782000005245209},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.2605000138282776},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.2524000108242035}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/18m1177445","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1177445","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:1803.10068","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1803.10068","pdf_url":"https://arxiv.org/pdf/1803.10068","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-01745366v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01745366","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 Journal on Numerical Analysis, 2019, 57 (2), pp.657-680. &#x27E8;10.1137/18M1177445&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1803.10068","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1803.10068","pdf_url":"https://arxiv.org/pdf/1803.10068","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3339920443","display_name":null,"funder_award_id":"R-146-000-223-112","funder_id":"https://openalex.org/F4320320751","funder_display_name":"Ministry of Education - Singapore"},{"id":"https://openalex.org/G3597637701","display_name":"Centre de Math\u00e9matiques Henri Lebesgue : fondements, interactions, applications et Formation","funder_award_id":"ANR-11-LABX-0020","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G4620322652","display_name":null,"funder_award_id":"YJ201807","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G7349311924","display_name":null,"funder_award_id":"MOE2015-T2-2-146","funder_id":"https://openalex.org/F4320320751","funder_display_name":"Ministry of Education - Singapore"}],"funders":[{"id":"https://openalex.org/F4320320751","display_name":"Ministry of Education - Singapore","ror":"https://ror.org/01kcva023"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1964470050","https://openalex.org/W1973929353","https://openalex.org/W1993142553","https://openalex.org/W2005105370","https://openalex.org/W2012618218","https://openalex.org/W2020107848","https://openalex.org/W2023403160","https://openalex.org/W2028813971","https://openalex.org/W2060171999","https://openalex.org/W2061904552","https://openalex.org/W2066944044","https://openalex.org/W2071357402","https://openalex.org/W2076523251","https://openalex.org/W2078210968","https://openalex.org/W2083561837","https://openalex.org/W2086524222","https://openalex.org/W2088629022","https://openalex.org/W2111755943","https://openalex.org/W2169053604","https://openalex.org/W2171594451","https://openalex.org/W2312961750","https://openalex.org/W2563583896","https://openalex.org/W2777140346"],"related_works":[],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,75,82,105],"regularized":[3,76],"finite":[4,107],"difference":[5,108],"method":[6,109],"for":[7,61,112],"the":[8,20,23,36,41,62,68,94,114,124,135],"logarithmic":[9,24],"Schr\u00f6dinger":[10],"equation":[11],"(LogSE)":[12],"and":[13,38,56,71,88,98,116,128],"establish":[14],"its":[15],"error":[16,59,70,117,148],"bound.":[17],"Due":[18],"to":[19,66,72,145],"blowup":[21],"of":[22,96,102,123],"nonlinearity,":[25],"i.e.,":[26],"$\\ln":[27],"\\rho\\to":[28],"-\\infty$":[29],"when":[30],"$\\rho\\rightarrow":[31],"0^+$":[32],"with":[33,81],"$\\rho=|u|^2$":[34],"being":[35,40],"density":[37],"$u$":[39],"complex-valued":[42],"wave":[43],"function":[44],"or":[45],"order":[46,65],"parameter,":[47],"there":[48],"are":[49,119,143],"significant":[50],"difficulties":[51],"in":[52,100,121],"designing":[53],"numerical":[54,141],"methods":[55],"establishing":[57],"their":[58],"bounds":[60],"LogSE.":[63],"In":[64],"suppress":[67],"roundoff":[69],"avoid":[73],"blowup,":[74],"LogSE":[77,99],"(RLogSE)":[78],"is":[79,91,110],"proposed":[80],"small":[83,136],"regularization":[84,137],"parameter":[85,138],"$0<\\varepsilon\\ll":[86],"1$":[87],"linear":[89],"convergence":[90],"established":[92,120],"between":[93],"solutions":[95],"RLogSE":[97,115],"term":[101],"$\\varepsilon$.":[103,139],"Then":[104],"semi-implicit":[106],"presented":[111],"discretizing":[113],"estimates":[118],"terms":[122],"mesh":[125],"size":[126],"$h$":[127],"time":[129],"step":[130],"$\\tau$":[131],"as":[132,134],"well":[133],"Finally":[140],"results":[142],"reported":[144],"illustrate":[146],"our":[147],"bounds.":[149]},"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1}],"updated_date":"2026-06-22T08:00:12.763002","created_date":"2018-04-06T00:00:00"}
