{"id":"https://openalex.org/W2011033548","doi":"https://doi.org/10.1137/s1064827599363381","title":"Collocation Methods for the Computation of Periodic Solutions of Delay Differential Equations","display_name":"Collocation Methods for the Computation of Periodic Solutions of Delay Differential Equations","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2011033548","doi":"https://doi.org/10.1137/s1064827599363381","mag":"2011033548"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827599363381","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827599363381","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5050679693","display_name":"Koen Engelborghs","orcid":null},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"K. Engelborghs","raw_affiliation_strings":[", KU Leuven"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":", KU Leuven","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072166085","display_name":"Tatyana Luzyanina","orcid":"https://orcid.org/0000-0002-3586-6563"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"T. Luzyanina","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018319998","display_name":"Karel J. in \u2019t Hout","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"K. J. In 't Hout","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5066002298","display_name":"Dirk Roose","orcid":"https://orcid.org/0000-0003-3758-9501"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"D. Roose","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":12.434,"has_fulltext":false,"cited_by_count":121,"citation_normalized_percentile":{"value":0.99212598,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"22","issue":"5","first_page":"1593","last_page":"1609"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9998000264167786,"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/T12727","display_name":"Differential Equations and Numerical Methods","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/T11416","display_name":"Numerical methods for differential equations","score":0.9990000128746033,"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":0.9927999973297119,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7825000286102295},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.7227533459663391},{"id":"https://openalex.org/keywords/superconvergence","display_name":"Superconvergence","score":0.7074678540229797},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.7047379016876221},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6583857536315918},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6456423997879028},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5982214212417603},{"id":"https://openalex.org/keywords/orthogonal-collocation","display_name":"Orthogonal collocation","score":0.58274245262146},{"id":"https://openalex.org/keywords/delay-differential-equation","display_name":"Delay differential equation","score":0.5226535797119141},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5091859698295593},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5034992098808289},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4655495584011078},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4494469165802002},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.43998983502388},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.43828481435775757},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3812773823738098},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.37787580490112305},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.23159030079841614},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14102566242218018},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11809885501861572}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7825000286102295},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.7227533459663391},{"id":"https://openalex.org/C83295009","wikidata":"https://www.wikidata.org/wiki/Q7643190","display_name":"Superconvergence","level":3,"score":0.7074678540229797},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.7047379016876221},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6583857536315918},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6456423997879028},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5982214212417603},{"id":"https://openalex.org/C114609681","wikidata":"https://www.wikidata.org/wiki/Q24839227","display_name":"Orthogonal collocation","level":5,"score":0.58274245262146},{"id":"https://openalex.org/C147504518","wikidata":"https://www.wikidata.org/wiki/Q2146125","display_name":"Delay differential equation","level":3,"score":0.5226535797119141},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5091859698295593},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5034992098808289},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4655495584011078},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4494469165802002},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.43998983502388},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.43828481435775757},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3812773823738098},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.37787580490112305},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.23159030079841614},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14102566242218018},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11809885501861572},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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":2,"locations":[{"id":"doi:10.1137/s1064827599363381","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827599363381","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.34.3232","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.34.3232","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.leidenuniv.nl/~hout/tw295.ps.gz","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.5}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1533456237","https://openalex.org/W1568666422","https://openalex.org/W1963570328","https://openalex.org/W1968521828","https://openalex.org/W1973877138","https://openalex.org/W1998927467","https://openalex.org/W2007828458","https://openalex.org/W2010390180","https://openalex.org/W2012478756","https://openalex.org/W2015898169","https://openalex.org/W2036663938","https://openalex.org/W2043191176","https://openalex.org/W2047017331","https://openalex.org/W2047929780","https://openalex.org/W2050514626","https://openalex.org/W2055614104","https://openalex.org/W2056023300","https://openalex.org/W2057059553","https://openalex.org/W2071370044","https://openalex.org/W2072559684","https://openalex.org/W2113479572","https://openalex.org/W4255754126"],"related_works":["https://openalex.org/W2045953892","https://openalex.org/W4384829779","https://openalex.org/W2032662168","https://openalex.org/W2622617724","https://openalex.org/W1597492899","https://openalex.org/W105826708","https://openalex.org/W1985051213","https://openalex.org/W3021297805","https://openalex.org/W2027593929","https://openalex.org/W2800153627"],"abstract_inverted_index":{"In":[0,88],"this":[1],"paper":[2],"we":[3,90],"investigate":[4,48],"collocation":[5,50,115],"methods":[6,51],"for":[7,36,82,86],"the":[8,41,95,105,112],"computation":[9],"of":[10,13,43,64,70,114,123],"periodic":[11,26],"solutions":[12,20],"autonomous":[14],"delay":[15],"differential":[16,45],"equations":[17],"(DDEs).":[18],"Periodic":[19],"are":[21],"found":[22],"by":[23],"solving":[24],"a":[25,120],"two-point":[27],"boundary":[28],"value":[29,84],"problem,":[30],"which":[31],"is":[32],"an":[33,67],"infinite-dimensional":[34],"problem":[35],"DDEs,":[37],"in":[38],"contrast":[39],"to":[40],"case":[42],"ordinary":[44],"equations.":[46],"We":[47,56,72,117],"three":[49],"based":[52],"on":[53,104,111],"piecewise":[54],"polynomials.":[55],"discuss":[57],"computational":[58],"issues":[59],"and":[60,110],"show":[61,91],"numerical":[62,75],"orders":[63],"convergence":[65,80],"using":[66],"extensive":[68],"number":[69],"tests.":[71],"compare":[73],"our":[74],"results":[76,81],"with":[77,119],"known":[78],"theoretical":[79],"initial":[83],"problems":[85],"DDEs.":[87],"particular,":[89],"how":[92],"superconvergence":[93],"at":[94],"mesh":[96,125],"points":[97],"can":[98],"be":[99],"lost":[100],"or":[101],"recovered":[102],"depending":[103],"DDE":[106],"model":[107],"under":[108],"consideration":[109],"choice":[113],"discretization.":[116],"end":[118],"brief":[121],"discussion":[122],"adaptive":[124],"selection.":[126]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":7}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
