{"id":"https://openalex.org/W1971170512","doi":"https://doi.org/10.1137/040612452","title":"Piecewise Polynomial Collocation for Fredholm Integro-Differential Equations with Weakly Singular Kernels","display_name":"Piecewise Polynomial Collocation for Fredholm Integro-Differential Equations with Weakly Singular Kernels","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W1971170512","doi":"https://doi.org/10.1137/040612452","mag":"1971170512"},"language":"en","primary_location":{"id":"doi:10.1137/040612452","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040612452","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/A5006816346","display_name":"Inga Parts","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Inga Parts","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023517944","display_name":"Arvet Pedas","orcid":"https://orcid.org/0000-0003-4331-3181"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Arvet Pedas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5033938200","display_name":"Enn Tamme","orcid":"https://orcid.org/0000-0002-0504-9044"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Enn Tamme","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":0.5966,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.74874829,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"43","issue":"5","first_page":"1897","last_page":"1911"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9991000294685364,"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":0.9991000294685364,"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":0.9965999722480774,"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"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9951000213623047,"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":0.9025397896766663},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.7831602096557617},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.6635035276412964},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.615146279335022},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6132023930549622},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6118330359458923},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.568652331829071},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5547067523002625},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47633296251296997},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.4739016592502594},{"id":"https://openalex.org/keywords/fredholm-integral-equation","display_name":"Fredholm integral equation","score":0.46617746353149414},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4537326693534851},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.3525225818157196}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9025397896766663},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.7831602096557617},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.6635035276412964},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.615146279335022},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6132023930549622},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6118330359458923},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.568652331829071},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5547067523002625},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47633296251296997},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.4739016592502594},{"id":"https://openalex.org/C89285879","wikidata":"https://www.wikidata.org/wiki/Q2991898","display_name":"Fredholm integral equation","level":3,"score":0.46617746353149414},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4537326693534851},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.3525225818157196},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C62649853","wikidata":"https://www.wikidata.org/wiki/Q199687","display_name":"Remote sensing","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/040612452","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040612452","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W27617868","https://openalex.org/W75830598","https://openalex.org/W1567668233","https://openalex.org/W1593659839","https://openalex.org/W1602369757","https://openalex.org/W1967818484","https://openalex.org/W1986676092","https://openalex.org/W1986683394","https://openalex.org/W1988932741","https://openalex.org/W1989764105","https://openalex.org/W1993080951","https://openalex.org/W2006373179","https://openalex.org/W2014208709","https://openalex.org/W2028224531","https://openalex.org/W2031625690","https://openalex.org/W2041584502","https://openalex.org/W2047136919","https://openalex.org/W2050329902","https://openalex.org/W2060819023","https://openalex.org/W2065496958","https://openalex.org/W2067027858","https://openalex.org/W2073689707","https://openalex.org/W2131147916","https://openalex.org/W2163965290","https://openalex.org/W3004569385","https://openalex.org/W3134067276","https://openalex.org/W4239688777","https://openalex.org/W4250243937","https://openalex.org/W4253832939","https://openalex.org/W4292232969"],"related_works":["https://openalex.org/W2536379864","https://openalex.org/W3093556794","https://openalex.org/W3021297805","https://openalex.org/W631163165","https://openalex.org/W1969157313","https://openalex.org/W2034622590","https://openalex.org/W395577430","https://openalex.org/W2015085231","https://openalex.org/W2549423735","https://openalex.org/W2810224196"],"abstract_inverted_index":{"In":[0],"the":[1,9,37,54,57,65,68,80,84],"first":[2],"part":[3],"of":[4,12,14,19,39,53,59,67,71,73,79,83],"this":[5],"paper":[6,55],"we":[7],"study":[8],"regularity":[10],"properties":[11],"solutions":[13,75],"initial-":[15],"or":[16,27],"boundary-value":[17],"problems":[18,48],"linear":[20],"Fredholm":[21],"integro-differential":[22],"equations":[23],"with":[24],"weakly":[25],"singular":[26],"other":[28],"nonsmooth":[29],"kernels.":[30],"We":[31],"then":[32],"use":[33],"these":[34],"results":[35],"in":[36],"analysis":[38,66],"a":[40],"piecewise":[41],"polynomial":[42],"collocation":[43],"method":[44],"for":[45,76],"solving":[46],"such":[47],"numerically.":[49],"The":[50],"main":[51],"purpose":[52],"is":[56],"derivation":[58],"optimal":[60],"global":[61],"convergence":[62,72],"estimates":[63],"and":[64],"attainable":[69],"order":[70],"numerical":[74],"all":[77],"values":[78],"nonuniformity":[81],"parameter":[82],"underlying":[85],"grid.":[86]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}