{"id":"https://openalex.org/W2979244352","doi":"https://doi.org/10.1007/s40314-019-0946-x","title":"Approximate solutions of Volterra integral equations by an interpolation method based on ramp functions","display_name":"Approximate solutions of Volterra integral equations by an interpolation method based on ramp functions","publication_year":2019,"publication_date":"2019-10-03","ids":{"openalex":"https://openalex.org/W2979244352","doi":"https://doi.org/10.1007/s40314-019-0946-x","mag":"2979244352"},"language":"en","primary_location":{"id":"doi:10.1007/s40314-019-0946-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-019-0946-x","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"1807-0302","issn":["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/A5080013307","display_name":"Danilo Costarell\u0131","orcid":"https://orcid.org/0000-0001-8834-8877"},"institutions":[{"id":"https://openalex.org/I27483092","display_name":"University of Perugia","ror":"https://ror.org/00x27da85","country_code":"IT","type":"education","lineage":["https://openalex.org/I27483092"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Danilo Costarelli","raw_affiliation_strings":["Department of Mathematics and Computer Science, University of Perugia, 1, Via Vanvitelli, 06123, Perugia, Italy"],"raw_orcid":"https://orcid.org/0000-0001-8834-8877","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, University of Perugia, 1, Via Vanvitelli, 06123, Perugia, Italy","institution_ids":["https://openalex.org/I27483092"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5080013307"],"corresponding_institution_ids":["https://openalex.org/I27483092"],"apc_list":null,"apc_paid":null,"fwci":0.681,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.68871117,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"38","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":0.9994999766349792,"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/T12661","display_name":"Iterative Methods for Nonlinear 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/T11191","display_name":"Mathematical functions and polynomials","score":0.9958999752998352,"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/volterra-integral-equation","display_name":"Volterra integral equation","score":0.7586602568626404},{"id":"https://openalex.org/keywords/heaviside-step-function","display_name":"Heaviside step function","score":0.746814489364624},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7129921317100525},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.7108086943626404},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.6601537466049194},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.6565337181091309},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.5803671479225159},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5308951735496521},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5214747190475464},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4720726013183594},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42926862835884094},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1873580813407898},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.09695133566856384},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.05935385823249817}],"concepts":[{"id":"https://openalex.org/C21965488","wikidata":"https://www.wikidata.org/wiki/Q2632613","display_name":"Volterra integral equation","level":3,"score":0.7586602568626404},{"id":"https://openalex.org/C7980502","wikidata":"https://www.wikidata.org/wiki/Q322339","display_name":"Heaviside step function","level":2,"score":0.746814489364624},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7129921317100525},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.7108086943626404},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.6601537466049194},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.6565337181091309},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.5803671479225159},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5308951735496521},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5214747190475464},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4720726013183594},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42926862835884094},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1873580813407898},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.09695133566856384},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.05935385823249817},{"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/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","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/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0},{"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s40314-019-0946-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-019-0946-x","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"1807-0302","issn":["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":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320333369","display_name":"Gruppo Nazionale per l'Analisi Matematica, la Probabilit\u00e0 e le loro Applicazioni","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W191236717","https://openalex.org/W1563225254","https://openalex.org/W1567668233","https://openalex.org/W1966332405","https://openalex.org/W1981044300","https://openalex.org/W1986164709","https://openalex.org/W1993003010","https://openalex.org/W2008021860","https://openalex.org/W2014208709","https://openalex.org/W2020988386","https://openalex.org/W2038266964","https://openalex.org/W2041793405","https://openalex.org/W2057700945","https://openalex.org/W2058949080","https://openalex.org/W2068802376","https://openalex.org/W2070896901","https://openalex.org/W2076063813","https://openalex.org/W2079131035","https://openalex.org/W2087293778","https://openalex.org/W2094724765","https://openalex.org/W2323427369","https://openalex.org/W2406122930","https://openalex.org/W2436103560","https://openalex.org/W2502087804","https://openalex.org/W2537866133","https://openalex.org/W2585014300","https://openalex.org/W2614181593","https://openalex.org/W2742489936","https://openalex.org/W2785811489","https://openalex.org/W2790159265","https://openalex.org/W2891995740","https://openalex.org/W2908062136","https://openalex.org/W2924037144","https://openalex.org/W2947825288","https://openalex.org/W2992305672","https://openalex.org/W3098453372","https://openalex.org/W3104090361","https://openalex.org/W4205354563","https://openalex.org/W4252219081"],"related_works":["https://openalex.org/W2118560105","https://openalex.org/W2048812671","https://openalex.org/W2358959122","https://openalex.org/W2078318892","https://openalex.org/W4225984655","https://openalex.org/W2031624200","https://openalex.org/W2791210196","https://openalex.org/W1987365920","https://openalex.org/W1826865795","https://openalex.org/W325682659"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4}],"updated_date":"2026-05-08T15:41:06.802602","created_date":"2025-10-10T00:00:00"}