{"id":"https://openalex.org/W2048763403","doi":"https://doi.org/10.1137/040615705","title":"Optimal Superconvergence Orders of Iterated Collocation Solutions for Volterra Integral Equations with Vanishing Delays","display_name":"Optimal Superconvergence Orders of Iterated Collocation Solutions for Volterra Integral Equations with Vanishing Delays","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2048763403","doi":"https://doi.org/10.1137/040615705","mag":"2048763403"},"language":"en","primary_location":{"id":"doi:10.1137/040615705","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040615705","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/A5031788253","display_name":"Hermann Brunner","orcid":"https://orcid.org/0000-0002-0089-3481"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hermann Brunner","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5047827167","display_name":"Qiya Hu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Qiya Hu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0882,"has_fulltext":false,"cited_by_count":33,"citation_normalized_percentile":{"value":0.88074647,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"43","issue":"5","first_page":"1934","last_page":"1949"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9994999766349792,"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"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9994000196456909,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/superconvergence","display_name":"Superconvergence","score":0.9848455190658569},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8687950372695923},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.6668733358383179},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6435150504112244},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.62132728099823},{"id":"https://openalex.org/keywords/volterra-integral-equation","display_name":"Volterra integral equation","score":0.6129492521286011},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.5831212997436523},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.4771815538406372},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4393080472946167},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42683082818984985},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.15255683660507202},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.10631793737411499}],"concepts":[{"id":"https://openalex.org/C83295009","wikidata":"https://www.wikidata.org/wiki/Q7643190","display_name":"Superconvergence","level":3,"score":0.9848455190658569},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8687950372695923},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.6668733358383179},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6435150504112244},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.62132728099823},{"id":"https://openalex.org/C21965488","wikidata":"https://www.wikidata.org/wiki/Q2632613","display_name":"Volterra integral equation","level":3,"score":0.6129492521286011},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.5831212997436523},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.4771815538406372},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4393080472946167},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42683082818984985},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.15255683660507202},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.10631793737411499},{"id":"https://openalex.org/C62649853","wikidata":"https://www.wikidata.org/wiki/Q199687","display_name":"Remote sensing","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},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/040615705","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040615705","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W75478609","https://openalex.org/W368825891","https://openalex.org/W1567668233","https://openalex.org/W1606942750","https://openalex.org/W1975516705","https://openalex.org/W1981554226","https://openalex.org/W1985051213","https://openalex.org/W1986683394","https://openalex.org/W1990514217","https://openalex.org/W2005238669","https://openalex.org/W2007828458","https://openalex.org/W2016883496","https://openalex.org/W2037269269","https://openalex.org/W2050329902","https://openalex.org/W2090402711","https://openalex.org/W2094250736","https://openalex.org/W2142338126","https://openalex.org/W2160118749","https://openalex.org/W3003736477","https://openalex.org/W3004569385","https://openalex.org/W4253848581","https://openalex.org/W4255754126"],"related_works":["https://openalex.org/W2059692408","https://openalex.org/W2569604312","https://openalex.org/W2045953892","https://openalex.org/W2078318892","https://openalex.org/W2032662168","https://openalex.org/W2067027858","https://openalex.org/W3126297227","https://openalex.org/W2022639369","https://openalex.org/W2185215189","https://openalex.org/W2066330736"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"analyze":[4],"the":[5,19,29,33,36,44,61,66,73,80,83,98,121],"optimal":[6,99],"convergence":[7],"properties":[8],"of":[9,14,18,28,35,46,50,76,82,118,124],"collocation":[10,38,42,63],"approximations":[11],"to":[12,41,92],"solutions":[13],"Volterra":[15,128],"integral":[16,129],"equations":[17,130],"second":[20],"kind":[21],"with":[22,94,136],"vanishing":[23],"variable":[24],"delays.":[25,96],"The":[26],"focus":[27],"analysis":[30],"is":[31],"on":[32,58],"superconvergence":[34,68,78,126],"(iterated)":[37],"approximation":[39],"corresponding":[40],"in":[43,89],"space":[45],"(discontinuous)":[47],"piecewise":[48],"polynomials":[49],"degree":[51],"$m-1":[52],"\\geq":[53],"0$.":[54],"We":[55],"show":[56],"that":[57,72],"uniform":[59],"meshes":[60],"iterated":[62],"solution":[64],"possesses":[65],"global":[67],"order":[69,75,100,123],"$m+1$,":[70],"and":[71],"solution's":[74],"local":[77,125],"at":[79],"nodes":[81],"underlying":[84],"mesh":[85],"cannot":[86],"exceed":[87],"$m+2$,":[88],"sharp":[90],"contrast":[91],"problems":[93],"nonvanishing":[95],"Moreover,":[97],"$p^{\\ast":[101],"}":[102],"=":[103],"m+2$":[104],"can":[105],"be":[106],"attained":[107],"only":[108],"under":[109],"suitable":[110],"assumptions.":[111],"This":[112],"result":[113],"also":[114],"resolves":[115],"a":[116,132],"conjecture":[117],"1997":[119],"regarding":[120],"attainable":[122],"for":[127],"containing":[131],"proportional":[133],"delay":[134],"$qt$":[135],"$q":[137],"\\in":[138],"(0,1)$.":[139]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}