{"id":"https://openalex.org/W4389451670","doi":"https://doi.org/10.1007/s10444-023-10094-4","title":"Piecewise orthogonal collocation for computing periodic solutions of renewal equations","display_name":"Piecewise orthogonal collocation for computing periodic solutions of renewal equations","publication_year":2023,"publication_date":"2023-12-01","ids":{"openalex":"https://openalex.org/W4389451670","doi":"https://doi.org/10.1007/s10444-023-10094-4"},"language":"en","primary_location":{"id":"doi:10.1007/s10444-023-10094-4","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s10444-023-10094-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10444-023-10094-4.pdf","source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10444-023-10094-4.pdf","any_repository_has_fulltext":false},"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"]},{"id":"https://openalex.org/I4210150763","display_name":"Gran Sasso Science Institute","ror":"https://ror.org/043qcb444","country_code":"IT","type":"education","lineage":["https://openalex.org/I160013858","https://openalex.org/I4210150763"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Alessia And\u00f2","raw_affiliation_strings":["Area of Mathematics, Gran Sasso Science Institute, Via Francesco Crispi, 7, 67100, L\u2019Aquila, Italy","CDLab \u2013 Computational Dynamics Laboratory, Department of Mathematics, Computer Science and Physics, University of Udine, Via delle Scienze, 206, 33100, Udine, Italy"],"raw_orcid":"https://orcid.org/0000-0002-4051-2049","affiliations":[{"raw_affiliation_string":"Area of Mathematics, Gran Sasso Science Institute, Via Francesco Crispi, 7, 67100, L\u2019Aquila, Italy","institution_ids":["https://openalex.org/I4210150763"]},{"raw_affiliation_string":"CDLab \u2013 Computational Dynamics Laboratory, Department of Mathematics, Computer Science and Physics, University of Udine, Via delle Scienze, 206, 33100, Udine, Italy","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":["CDLab \u2013 Computational Dynamics Laboratory, Department of Mathematics, Computer Science and Physics, University of Udine, Via delle Scienze, 206, 33100, Udine, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CDLab \u2013 Computational Dynamics Laboratory, Department of Mathematics, Computer Science and Physics, University of Udine, Via delle Scienze, 206, 33100, Udine, Italy","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","https://openalex.org/I4210150763"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.2156,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.51765674,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"49","issue":"6","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":0.9987000226974487,"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"}},"topics":[{"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"}},{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9940999746322632,"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/piecewise","display_name":"Piecewise","score":0.8058450222015381},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.7356631755828857},{"id":"https://openalex.org/keywords/computational-science-and-engineering","display_name":"Computational Science and Engineering","score":0.7103523015975952},{"id":"https://openalex.org/keywords/orthogonal-collocation","display_name":"Orthogonal collocation","score":0.6768001317977905},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6739488244056702},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5914748311042786},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5717084407806396},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5361449718475342},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.531771719455719},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3159148693084717},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2759721279144287},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.24469563364982605},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.15392625331878662},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.09585943818092346}],"concepts":[{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.8058450222015381},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.7356631755828857},{"id":"https://openalex.org/C68597687","wikidata":"https://www.wikidata.org/wiki/Q362601","display_name":"Computational Science and Engineering","level":2,"score":0.7103523015975952},{"id":"https://openalex.org/C114609681","wikidata":"https://www.wikidata.org/wiki/Q24839227","display_name":"Orthogonal collocation","level":5,"score":0.6768001317977905},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6739488244056702},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5914748311042786},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5717084407806396},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5361449718475342},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.531771719455719},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3159148693084717},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2759721279144287},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.24469563364982605},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.15392625331878662},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.09585943818092346},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10444-023-10094-4","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s10444-023-10094-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10444-023-10094-4.pdf","source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s10444-023-10094-4","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s10444-023-10094-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10444-023-10094-4.pdf","source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.46000000834465027}],"awards":[{"id":"https://openalex.org/G995423422","display_name":null,"funder_award_id":"E15F21005420006","funder_id":"https://openalex.org/F4320331528","funder_display_name":"Ministero dell'Universit\u00e0 e della Ricerca"}],"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/F4320331528","display_name":"Ministero dell'Universit\u00e0 e della Ricerca","ror":null},{"id":"https://openalex.org/F4320334079","display_name":"Gruppo Nazionale per il Calcolo Scientifico","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4389451670.pdf"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W120167774","https://openalex.org/W1490180844","https://openalex.org/W1494118823","https://openalex.org/W1495343258","https://openalex.org/W1533456237","https://openalex.org/W1783677089","https://openalex.org/W1971751506","https://openalex.org/W1972729931","https://openalex.org/W1973877138","https://openalex.org/W2005261819","https://openalex.org/W2011033548","https://openalex.org/W2036350807","https://openalex.org/W2045055369","https://openalex.org/W2117060314","https://openalex.org/W2126076281","https://openalex.org/W2175328788","https://openalex.org/W2236801637","https://openalex.org/W2576881723","https://openalex.org/W2804285351","https://openalex.org/W2809460247","https://openalex.org/W3001465095","https://openalex.org/W3021297805","https://openalex.org/W3068323327","https://openalex.org/W3095740892","https://openalex.org/W3157943158","https://openalex.org/W3198509480","https://openalex.org/W4210960242","https://openalex.org/W4211202937","https://openalex.org/W4251579377"],"related_works":["https://openalex.org/W2791210196","https://openalex.org/W2078318892","https://openalex.org/W4255016916","https://openalex.org/W2111003632","https://openalex.org/W2889856026","https://openalex.org/W1987365920","https://openalex.org/W1989122168","https://openalex.org/W2000247808","https://openalex.org/W2384941625","https://openalex.org/W2060099884"],"abstract_inverted_index":{"Abstract":[0],"We":[1,24],"extend":[2],"the":[3,39],"use":[4],"of":[5,13,45,49],"piecewise":[6],"orthogonal":[7],"collocation":[8],"to":[9],"computing":[10],"periodic":[11],"solutions":[12],"renewal":[14],"equations,":[15],"which":[16],"are":[17],"particularly":[18],"important":[19],"in":[20,47],"modeling":[21],"population":[22],"dynamics.":[23],"prove":[25],"convergence":[26],"through":[27],"a":[28,43],"rigorous":[29],"error":[30],"analysis.":[31,51],"Finally,":[32],"we":[33],"show":[34],"some":[35],"numerical":[36],"experiments":[37],"confirming":[38],"theoretical":[40],"results":[41],"and":[42],"couple":[44],"applications":[46],"view":[48],"bifurcation":[50]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-01-24T23:23:39.755997","created_date":"2025-10-10T00:00:00"}