{"id":"https://openalex.org/W3068323327","doi":"https://doi.org/10.1137/19m1295015","title":"Convergence Analysis of Collocation Methods for Computing Periodic Solutions of Retarded Functional Differential Equations","display_name":"Convergence Analysis of Collocation Methods for Computing Periodic Solutions of Retarded Functional Differential Equations","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3068323327","doi":"https://doi.org/10.1137/19m1295015","mag":"3068323327"},"language":"en","primary_location":{"id":"doi:10.1137/19m1295015","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1295015","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/2008.07604","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036438633","display_name":"Alessia And\u00f2","orcid":"https://orcid.org/0000-0002-4051-2049"},"institutions":[{"id":"https://openalex.org/I129043915","display_name":"University of Udine","ror":"https://ror.org/05ht0mh31","country_code":"IT","type":"education","lineage":["https://openalex.org/I129043915"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Alessia And\u00f2","raw_affiliation_strings":["University of Udine"],"affiliations":[{"raw_affiliation_string":"University of Udine","institution_ids":["https://openalex.org/I129043915"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080897837","display_name":"Dimitri Breda","orcid":"https://orcid.org/0000-0002-4641-1126"},"institutions":[{"id":"https://openalex.org/I129043915","display_name":"University of Udine","ror":"https://ror.org/05ht0mh31","country_code":"IT","type":"education","lineage":["https://openalex.org/I129043915"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Dimitri Breda","raw_affiliation_strings":["University of Udine"],"affiliations":[{"raw_affiliation_string":"University of Udine","institution_ids":["https://openalex.org/I129043915"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5036438633"],"corresponding_institution_ids":["https://openalex.org/I129043915"],"apc_list":null,"apc_paid":null,"fwci":2.9553,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.9115536,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"58","issue":"5","first_page":"3010","last_page":"3039"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9997000098228455,"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/T12727","display_name":"Differential Equations and Numerical Methods","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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/piecewise","display_name":"Piecewise","score":0.8036435842514038},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.7787222862243652},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6583141088485718},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.637969434261322},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.5274108648300171},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5218064785003662},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5217031836509705},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49468204379081726},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4942176640033722},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.47880253195762634},{"id":"https://openalex.org/keywords/orthogonal-collocation","display_name":"Orthogonal collocation","score":0.43186473846435547},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4255942702293396},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.34013256430625916},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23260316252708435},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.19565051794052124},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12291765213012695}],"concepts":[{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.8036435842514038},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.7787222862243652},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6583141088485718},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.637969434261322},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.5274108648300171},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5218064785003662},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5217031836509705},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49468204379081726},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4942176640033722},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.47880253195762634},{"id":"https://openalex.org/C114609681","wikidata":"https://www.wikidata.org/wiki/Q24839227","display_name":"Orthogonal collocation","level":5,"score":0.43186473846435547},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4255942702293396},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.34013256430625916},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23260316252708435},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.19565051794052124},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12291765213012695},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/19m1295015","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1295015","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:2008.07604","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2008.07604","pdf_url":"https://arxiv.org/pdf/2008.07604","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":null,"raw_type":"text"},{"id":"pmh:oai:air.uniud.it:11390/1194967","is_oa":true,"landing_page_url":"http://hdl.handle.net/11390/1194967","pdf_url":null,"source":{"id":"https://openalex.org/S4306401163","display_name":"Institutional Research Information System (University of Udine)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I129043915","host_organization_name":"University of Udine","host_organization_lineage":["https://openalex.org/I129043915"],"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":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2008.07604","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2008.07604","pdf_url":"https://arxiv.org/pdf/2008.07604","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2436605503","display_name":null,"funder_award_id":"PRID 2017","funder_id":"https://openalex.org/F4320324979","funder_display_name":"Universit\u00e0 degli Studi di Udine"},{"id":"https://openalex.org/G8385760802","display_name":null,"funder_award_id":"PSD 2015 2017 DIMA PRID 2017 ZANOLIN","funder_id":"https://openalex.org/F4320324979","funder_display_name":"Universit\u00e0 degli Studi di Udine"}],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320324979","display_name":"Universit\u00e0 degli Studi di Udine","ror":null},{"id":"https://openalex.org/F4320334079","display_name":"Gruppo Nazionale per il Calcolo Scientifico","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W27422801","https://openalex.org/W573386291","https://openalex.org/W599878005","https://openalex.org/W1485916122","https://openalex.org/W1533456237","https://openalex.org/W1783677089","https://openalex.org/W1937028141","https://openalex.org/W1973877138","https://openalex.org/W1990442324","https://openalex.org/W1995557491","https://openalex.org/W1999103577","https://openalex.org/W2007407491","https://openalex.org/W2011033548","https://openalex.org/W2012478756","https://openalex.org/W2014898529","https://openalex.org/W2032206170","https://openalex.org/W2047017331","https://openalex.org/W2047929780","https://openalex.org/W2048017269","https://openalex.org/W2079871064","https://openalex.org/W2126076281","https://openalex.org/W2150770902","https://openalex.org/W2175328788","https://openalex.org/W2176995586","https://openalex.org/W2218418595","https://openalex.org/W2236801637","https://openalex.org/W2284323722","https://openalex.org/W2486484786","https://openalex.org/W2576881723","https://openalex.org/W2809460247","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2791210196","https://openalex.org/W2078318892","https://openalex.org/W4255016916","https://openalex.org/W2111003632","https://openalex.org/W2536379864","https://openalex.org/W1987365920","https://openalex.org/W2889856026","https://openalex.org/W1989122168","https://openalex.org/W2150070385","https://openalex.org/W2000247808"],"abstract_inverted_index":{"We":[0,54],"analyze":[1],"the":[2,19,86,89,105,113,126,134],"convergence":[3],"of":[4,12,88,107,128],"piecewise":[5],"collocation":[6],"methods":[7],"for":[8],"computing":[9],"periodic":[10,70],"solutions":[11],"general":[13],"retarded":[14],"functional":[15],"differential":[16],"equations":[17],"under":[18],"abstract":[20],"framework":[21],"recently":[22],"developed":[23],"in":[24,72],"[S.":[25,33,44],"Maset,":[26,34,45],"Numer.":[27,37,48],"Math.,":[28],"133":[29],"(2016),":[30],"pp.":[31,41,52],"525--555],":[32],"SIAM":[35,46],"J.":[36,47],"Anal.,":[38,49],"53":[39,50],"(2015),":[40,51],"2771--2793],":[42],"and":[43],"2794--2821].":[53],"rigorously":[55],"show":[56],"that":[57,112],"a":[58,61,66],"reformulation":[59],"as":[60,92,131,133],"boundary":[62,69],"value":[63],"problem":[64],"requires":[65],"proper":[67],"infinite-dimensional":[68],"condition":[71],"order":[73],"to":[74,77,104,123],"be":[75],"amenable":[76],"such":[78],"analysis.":[79],"In":[80],"this":[81,129],"regard,":[82],"we":[83,110,120],"also":[84],"highlight":[85],"role":[87],"period":[90],"acting":[91],"an":[93],"unknown":[94],"parameter,":[95],"which":[96],"is":[97,101,117,138],"critical":[98],"since":[99],"it":[100],"directly":[102],"linked":[103],"course":[106],"time.":[108],"Finally,":[109],"prove":[111],"finite":[114],"element":[115,136],"method":[116,137],"convergent,":[118],"while":[119],"limit":[121],"ourselves":[122],"commenting":[124],"on":[125],"infeasibility":[127],"approach":[130],"far":[132],"spectral":[135],"concerned.":[139]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2020-08-24T00:00:00"}