{"id":"https://openalex.org/W4281773171","doi":"https://doi.org/10.1007/s40314-022-01775-9","title":"Iterated collocation methods for nonlinear third-kind Volterra integral equations with proportional delays","display_name":"Iterated collocation methods for nonlinear third-kind Volterra integral equations with proportional delays","publication_year":2022,"publication_date":"2022-05-31","ids":{"openalex":"https://openalex.org/W4281773171","doi":"https://doi.org/10.1007/s40314-022-01775-9"},"language":"en","primary_location":{"id":"doi:10.1007/s40314-022-01775-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-022-01775-9","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"0101-8205","issn":["0101-8205","1807-0302","2238-3603"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Applied Mathematics","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/A5050176220","display_name":"Huiming Song","orcid":null},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huiming Song","raw_affiliation_strings":["School of Mathematics, Harbin Institute of Technology, Harbin, 150001, People\u2019s Republic of China","School of Mathematics, Harbin Institute of Technology, Harbin, 150001, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Harbin Institute of Technology, Harbin, 150001, People\u2019s Republic of China","institution_ids":["https://openalex.org/I204983213"]},{"raw_affiliation_string":"School of Mathematics, Harbin Institute of Technology, Harbin, 150001, People's Republic of China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040655215","display_name":"Zhanwen Yang","orcid":"https://orcid.org/0000-0001-6617-4642"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhanwen Yang","raw_affiliation_strings":["School of Mathematics, Harbin Institute of Technology, Harbin, 150001, People\u2019s Republic of China","School of Mathematics, Harbin Institute of Technology, Harbin, 150001, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Harbin Institute of Technology, Harbin, 150001, People\u2019s Republic of China","institution_ids":["https://openalex.org/I204983213"]},{"raw_affiliation_string":"School of Mathematics, Harbin Institute of Technology, Harbin, 150001, People's Republic of China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080746874","display_name":"Yu Xiao","orcid":"https://orcid.org/0000-0003-0269-0474"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yu Xiao","raw_affiliation_strings":["School of Mathematics, Harbin Institute of Technology, Harbin, 150001, People\u2019s Republic of China","School of Mathematics, Harbin Institute of Technology, Harbin, 150001, People's Republic of China"],"raw_orcid":"https://orcid.org/0000-0003-0269-0474","affiliations":[{"raw_affiliation_string":"School of Mathematics, Harbin Institute of Technology, Harbin, 150001, People\u2019s Republic of China","institution_ids":["https://openalex.org/I204983213"]},{"raw_affiliation_string":"School of Mathematics, Harbin Institute of Technology, Harbin, 150001, People's Republic of China","institution_ids":["https://openalex.org/I204983213"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5080746874"],"corresponding_institution_ids":["https://openalex.org/I204983213"],"apc_list":{"value":3090,"currency":"USD","value_usd":3090},"apc_paid":null,"fwci":1.0236,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.71228888,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"41","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9997000098228455,"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":0.9997000098228455,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9987999796867371,"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"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9965999722480774,"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/iterated-function","display_name":"Iterated function","score":0.8360583186149597},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.8047545552253723},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.799127459526062},{"id":"https://openalex.org/keywords/volterra-integral-equation","display_name":"Volterra integral equation","score":0.6371132135391235},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6355158090591431},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.618020236492157},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.616134762763977},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.585121750831604},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5432639122009277},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4343298375606537},{"id":"https://openalex.org/keywords/orthogonal-collocation","display_name":"Orthogonal collocation","score":0.4108372926712036},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.3738483786582947},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.10618704557418823},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09792840480804443},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.057949960231781006},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.045621275901794434}],"concepts":[{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.8360583186149597},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.8047545552253723},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.799127459526062},{"id":"https://openalex.org/C21965488","wikidata":"https://www.wikidata.org/wiki/Q2632613","display_name":"Volterra integral equation","level":3,"score":0.6371132135391235},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6355158090591431},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.618020236492157},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.616134762763977},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.585121750831604},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5432639122009277},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4343298375606537},{"id":"https://openalex.org/C114609681","wikidata":"https://www.wikidata.org/wiki/Q24839227","display_name":"Orthogonal collocation","level":5,"score":0.4108372926712036},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.3738483786582947},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.10618704557418823},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09792840480804443},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.057949960231781006},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.045621275901794434},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s40314-022-01775-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-022-01775-9","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"0101-8205","issn":["0101-8205","1807-0302","2238-3603"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.47999998927116394,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W771761315","https://openalex.org/W1567668233","https://openalex.org/W1998340996","https://openalex.org/W2007253236","https://openalex.org/W2020648078","https://openalex.org/W2036539190","https://openalex.org/W2048763403","https://openalex.org/W2059039541","https://openalex.org/W2060864910","https://openalex.org/W2472358980","https://openalex.org/W2480359983","https://openalex.org/W2540315472","https://openalex.org/W2765372099","https://openalex.org/W2912669820","https://openalex.org/W2917102097","https://openalex.org/W3132028146","https://openalex.org/W3163685554","https://openalex.org/W4236905297","https://openalex.org/W4252219081"],"related_works":["https://openalex.org/W2791210196","https://openalex.org/W4255016916","https://openalex.org/W2078318892","https://openalex.org/W2111003632","https://openalex.org/W2889856026","https://openalex.org/W1987365920","https://openalex.org/W1989122168","https://openalex.org/W2000247808","https://openalex.org/W144985429","https://openalex.org/W2384941625"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}