{"id":"https://openalex.org/W3000427044","doi":"https://doi.org/10.1137/18m1227536","title":"Long-time Accurate Symmetrized Implicit-explicit BDF Methods for a Class of Parabolic Equations with Non-self-adjoint Operators","display_name":"Long-time Accurate Symmetrized Implicit-explicit BDF Methods for a Class of Parabolic Equations with Non-self-adjoint Operators","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3000427044","doi":"https://doi.org/10.1137/18m1227536","mag":"3000427044"},"language":"en","primary_location":{"id":"doi:10.1137/18m1227536","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1227536","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"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039197834","display_name":"Buyang Li","orcid":"https://orcid.org/0000-0001-7566-3464"},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":true,"raw_author_name":"Buyang Li","raw_affiliation_strings":["The Hong Kong Polytechnic University"],"affiliations":[{"raw_affiliation_string":"The Hong Kong Polytechnic University","institution_ids":["https://openalex.org/I14243506"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100650570","display_name":"Kai Wang","orcid":"https://orcid.org/0000-0002-9219-875X"},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Kai Wang","raw_affiliation_strings":["The Hong Kong Polytechnic University"],"affiliations":[{"raw_affiliation_string":"The Hong Kong Polytechnic University","institution_ids":["https://openalex.org/I14243506"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002445122","display_name":"Zhi Zhou","orcid":"https://orcid.org/0000-0002-3439-0313"},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Zhi Zhou","raw_affiliation_strings":["The Hong Kong Polytechnic University"],"affiliations":[{"raw_affiliation_string":"The Hong Kong Polytechnic University","institution_ids":["https://openalex.org/I14243506"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5039197834"],"corresponding_institution_ids":["https://openalex.org/I14243506"],"apc_list":null,"apc_paid":null,"fwci":3.8448,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.93645251,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"58","issue":"1","first_page":"189","last_page":"210"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","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/T12727","display_name":"Differential Equations and Numerical Methods","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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9987000226974487,"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"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9983000159263611,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8761134147644043},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6434362530708313},{"id":"https://openalex.org/keywords/self-adjoint-operator","display_name":"Self-adjoint operator","score":0.5178294777870178},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5053554177284241},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5033270716667175},{"id":"https://openalex.org/keywords/linear-multistep-method","display_name":"Linear multistep method","score":0.4869183301925659},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4626067578792572},{"id":"https://openalex.org/keywords/backward-differentiation-formula","display_name":"Backward differentiation formula","score":0.43364182114601135},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.42611798644065857},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.4243970811367035},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.18105396628379822},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.10364881157875061}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8761134147644043},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6434362530708313},{"id":"https://openalex.org/C171972299","wikidata":"https://www.wikidata.org/wiki/Q6500908","display_name":"Self-adjoint operator","level":3,"score":0.5178294777870178},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5053554177284241},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5033270716667175},{"id":"https://openalex.org/C65889100","wikidata":"https://www.wikidata.org/wiki/Q1462003","display_name":"Linear multistep method","level":5,"score":0.4869183301925659},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4626067578792572},{"id":"https://openalex.org/C152522140","wikidata":"https://www.wikidata.org/wiki/Q795746","display_name":"Backward differentiation formula","level":5,"score":0.43364182114601135},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.42611798644065857},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.4243970811367035},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.18105396628379822},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.10364881157875061},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.0},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"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/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.0},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/18m1227536","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1227536","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:ira.lib.polyu.edu.hk:10397/89355","is_oa":false,"landing_page_url":"http://hdl.handle.net/10397/89355","pdf_url":null,"source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"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":"Journal/Magazine Article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.5600000023841858,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1968426797","https://openalex.org/W1973451700","https://openalex.org/W1993309344","https://openalex.org/W2000486121","https://openalex.org/W2025567273","https://openalex.org/W2027417374","https://openalex.org/W2030534447","https://openalex.org/W2031029580","https://openalex.org/W2032246227","https://openalex.org/W2035346182","https://openalex.org/W2043107210","https://openalex.org/W2050516929","https://openalex.org/W2058339183","https://openalex.org/W2058879110","https://openalex.org/W2061391294","https://openalex.org/W2063052319","https://openalex.org/W2075957684","https://openalex.org/W2078767654","https://openalex.org/W2084195801","https://openalex.org/W2088910140","https://openalex.org/W2097116154","https://openalex.org/W2104410771","https://openalex.org/W2107589277","https://openalex.org/W2110719162","https://openalex.org/W2147268354","https://openalex.org/W2273169098","https://openalex.org/W2515206481","https://openalex.org/W2601627861","https://openalex.org/W2612471483","https://openalex.org/W2764314153","https://openalex.org/W4232326701","https://openalex.org/W4234178278"],"related_works":["https://openalex.org/W2142285866","https://openalex.org/W2015517699","https://openalex.org/W3091448100","https://openalex.org/W2281892811","https://openalex.org/W1974047522","https://openalex.org/W2358336335","https://openalex.org/W2950222062","https://openalex.org/W1992198790","https://openalex.org/W1974749588","https://openalex.org/W2345925210"],"abstract_inverted_index":{"An":[0],"implicit-explicit":[1],"multistep":[2],"method":[3,72,124],"based":[4],"on":[5],"the":[6,30,36,49,63,70,76,79,85,101,107,114,122,131,137,171],"backward":[7],"difference":[8],"formulae":[9],"(BDF)":[10],"is":[11,73,81,88],"proposed":[12,123],"for":[13,29,69,116],"time":[14],"discretization":[15],"of":[16,35,118,136],"parabolic":[17],"equations":[18],"with":[19],"a":[20,40],"non-self-adjoint":[21,86],"operator.":[22],"Implicit":[23],"and":[24,32,83,125,161],"explicit":[25],"schemes":[26],"are":[27,46],"used":[28,112],"self-adjoint":[31],"anti-self-adjoint":[33],"parts":[34],"operator,":[37],"respectively.":[38],"For":[39],"$k$-step":[41],"method,":[42],"some":[43],"correction":[44],"terms":[45],"added":[47],"to":[48,53,158,166],"starting":[50],"$k-1$":[51],"steps":[52],"maintain":[54],"$k$th-order":[55,67],"convergence":[56,68],"without":[57],"imposing":[58],"further":[59],"compatibility":[60],"conditions":[61],"at":[62],"initial":[64],"time.":[65],"Long-time":[66],"numerical":[71],"proved":[74],"under":[75],"assumptions":[77],"that":[78,84],"operator":[80,93],"coercive":[82],"part":[87],"low":[89],"order.":[90],"Such":[91],"an":[92],"often":[94],"appears":[95],"in":[96,113,127,140],"practical":[97],"computation":[98],"(such":[99],"as":[100],"Stokes--Darcy":[102,138],"system)":[103],"but":[104],"may":[105],"violate":[106],"standard":[108],"sectorial":[109],"angle":[110],"condition":[111],"literature":[115],"analysis":[117,126,135],"BDF.":[119],"In":[120],"particular,":[121],"this":[128],"paper":[129],"extend":[130],"long-time":[132],"energy":[133],"error":[134],"system":[139],"Chen":[141],"et":[142],"al.":[143],"[SIAM":[144],"J.":[145],"Numer.":[146,152],"Anal.,":[147],"51":[148],"(2013),":[149],"pp.":[150,156],"2563--2584;":[151],"Math.,":[153],"134":[154],"(2016),":[155],"857--879]":[157],"general":[159],"symmetrized":[160],"decoupled":[162],"BDF":[163],"methods":[164],"up":[165],"order":[167],"6":[168],"by":[169],"using":[170],"generating":[172],"function":[173],"technique.":[174]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":7}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
