{"id":"https://openalex.org/W2155678956","doi":"https://doi.org/10.1080/00207160701411145","title":"Numerical solution of Urysohn integral equations using the iterated collocation method","display_name":"Numerical solution of Urysohn integral equations using the iterated collocation method","publication_year":2007,"publication_date":"2007-12-31","ids":{"openalex":"https://openalex.org/W2155678956","doi":"https://doi.org/10.1080/00207160701411145","mag":"2155678956"},"language":"en","primary_location":{"id":"doi:10.1080/00207160701411145","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160701411145","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer 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/A5032667200","display_name":"K. Maleknejad","orcid":"https://orcid.org/0000-0003-1774-7525"},"institutions":[{"id":"https://openalex.org/I67009956","display_name":"Iran University of Science and Technology","ror":"https://ror.org/01jw2p796","country_code":"IR","type":"education","lineage":["https://openalex.org/I67009956"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Khosrow Maleknejad","raw_affiliation_strings":["School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846, Iran","institution_ids":["https://openalex.org/I67009956"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004754956","display_name":"H. Derili","orcid":"https://orcid.org/0000-0001-5854-2249"},"institutions":[{"id":"https://openalex.org/I204588832","display_name":"Islamic Azad University, Karaj","ror":"https://ror.org/01y4xm534","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I204588832"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Hesamoddin Derili","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Islamic Azad University (Karaj Unit), Rajae Shahr, Karaj, 3149968111, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Islamic Azad University (Karaj Unit), Rajae Shahr, Karaj, 3149968111, Iran","institution_ids":["https://openalex.org/I204588832"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073377548","display_name":"S. Sohrabi","orcid":"https://orcid.org/0000-0002-0920-2747"},"institutions":[{"id":"https://openalex.org/I67009956","display_name":"Iran University of Science and Technology","ror":"https://ror.org/01jw2p796","country_code":"IR","type":"education","lineage":["https://openalex.org/I67009956"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Saeed Sohrabi","raw_affiliation_strings":["School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846, Iran","institution_ids":["https://openalex.org/I67009956"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5032667200"],"corresponding_institution_ids":["https://openalex.org/I67009956"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.12398158,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"85","issue":"1","first_page":"143","last_page":"154"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9987000226974487,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.998199999332428,"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/mathematics","display_name":"Mathematics","score":0.8552758693695068},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.7821898460388184},{"id":"https://openalex.org/keywords/superconvergence","display_name":"Superconvergence","score":0.778326153755188},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.6047855615615845},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.525027334690094},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5179144740104675},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5168095827102661},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.46080824732780457},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4579535722732544},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.4488098621368408},{"id":"https://openalex.org/keywords/orthogonal-collocation","display_name":"Orthogonal collocation","score":0.4247705638408661},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.31387367844581604},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2902368903160095},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.13830599188804626},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.1218409538269043},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.10174506902694702},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07107728719711304}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8552758693695068},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.7821898460388184},{"id":"https://openalex.org/C83295009","wikidata":"https://www.wikidata.org/wiki/Q7643190","display_name":"Superconvergence","level":3,"score":0.778326153755188},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.6047855615615845},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.525027334690094},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5179144740104675},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5168095827102661},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.46080824732780457},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4579535722732544},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.4488098621368408},{"id":"https://openalex.org/C114609681","wikidata":"https://www.wikidata.org/wiki/Q24839227","display_name":"Orthogonal collocation","level":5,"score":0.4247705638408661},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.31387367844581604},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2902368903160095},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.13830599188804626},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.1218409538269043},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.10174506902694702},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07107728719711304},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"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/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"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:10.1080/00207160701411145","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160701411145","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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":13,"referenced_works":["https://openalex.org/W1965386465","https://openalex.org/W1974562296","https://openalex.org/W1976349149","https://openalex.org/W1978142553","https://openalex.org/W1985307809","https://openalex.org/W1998227768","https://openalex.org/W2012163315","https://openalex.org/W2013984730","https://openalex.org/W2036064357","https://openalex.org/W2067027858","https://openalex.org/W2083144489","https://openalex.org/W2085063499","https://openalex.org/W2480176609"],"related_works":["https://openalex.org/W2045953892","https://openalex.org/W2791210196","https://openalex.org/W2185215189","https://openalex.org/W2078318892","https://openalex.org/W2031484768","https://openalex.org/W4255016916","https://openalex.org/W2111003632","https://openalex.org/W2032662168","https://openalex.org/W4384829779","https://openalex.org/W1987365920"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"analyse":[4,110],"the":[5,10,25,35,38,101,111,127,148],"iterated":[6,39,102],"collocation":[7,128],"method":[8,41,81],"for":[9,42,82,136],"nonlinear":[11],"operator":[12],"equation":[13],"x":[14,84,90],"=":[15,85,92],"y+K(x)":[16,86],"with":[17],"K":[18],"a":[19,60,71,122,137],"smooth":[20],"kernel.":[21],"The":[22,79],"paper":[23],"expands":[24],"study":[26],"begun":[27],"by":[28,89],"H.":[29],"Kaneko":[30],"and":[31,66,100,117],"Y.":[32],"Xu":[33],"concerning":[34],"superconvergence":[36,149],"of":[37,52,62,73,113,140,150],"Galerkin":[40],"Hammerstein":[43],"equations.":[44],"Let":[45,54],"x*":[46],"denote":[47,59],"an":[48],"isolated":[49],"fixed":[50],"point":[51],"K.":[53],"X":[55,74,76],"n":[56,69,77,91,94,96,98,115],",":[57],"n\u22651,":[58],"sequence":[61],"finite-dimensional":[63],"approximating":[64],"subspaces,":[65],"let":[67],"P":[68,93],"be":[70],"projection":[72,80,103],"onto":[75],".":[78,108],"solving":[83],"is":[87,105,133],"given":[88,135],"y+P":[95],"K(x":[97],"),":[99],"solution":[104],"defined":[106],"as":[107],"We":[109],"convergence":[112],"{x":[114],"}":[116],"{}":[118,151],"to":[119,152],"x*,":[120],"giving":[121],"general":[123],"analysis":[124,132],"that":[125],"includes":[126],"method.":[129],"A":[130],"detailed":[131],"then":[134],"large":[138],"class":[139],"Urysohn":[141],"integral":[142],"operators":[143],"in":[144],"one":[145],"variable,":[146],"showing":[147],"x*.":[153]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2026-08-15T07:11:24.734988","created_date":"2025-10-10T00:00:00"}