{"id":"https://openalex.org/W2075120572","doi":"https://doi.org/10.1080/00207160802123417","title":"The discrete collocation method for weakly singular Urysohn equations","display_name":"The discrete collocation method for weakly singular Urysohn equations","publication_year":2008,"publication_date":"2008-09-27","ids":{"openalex":"https://openalex.org/W2075120572","doi":"https://doi.org/10.1080/00207160802123417","mag":"2075120572"},"language":"en","primary_location":{"id":"doi:10.1080/00207160802123417","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160802123417","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/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":true,"raw_author_name":"K. Maleknejad","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Islamic Azad University (Karaj Branch), Karaj, Iran","Department of Mathematics, Faculty of Science, Islamic Azad University, Karaj branch, Karaj, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Islamic Azad University (Karaj Branch), Karaj, Iran","institution_ids":["https://openalex.org/I204588832"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Islamic Azad University, Karaj branch, Karaj, Iran","institution_ids":["https://openalex.org/I204588832"]}]},{"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":"H. Derili","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Islamic Azad University (Karaj Branch), Karaj, Iran","Department of Mathematics, Faculty of Science, Islamic Azad University, Karaj branch, Karaj, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Islamic Azad University (Karaj Branch), Karaj, Iran","institution_ids":["https://openalex.org/I204588832"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Islamic Azad University, Karaj branch, Karaj, 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":"S. Sohrabi","raw_affiliation_strings":["School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran","School of mathematics, Iran University of Science and Technology, Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran","institution_ids":["https://openalex.org/I67009956"]},{"raw_affiliation_string":"School of mathematics, Iran University of Science and Technology, Tehran, 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/I204588832"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.11210929,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"87","issue":"2","first_page":"404","last_page":"413"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9973000288009644,"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"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9973000288009644,"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"}},{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9966999888420105,"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":0.9939000010490417,"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":0.8777150511741638},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.7891544103622437},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.657253623008728},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.6347208619117737},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.595007061958313},{"id":"https://openalex.org/keywords/orthogonal-collocation","display_name":"Orthogonal collocation","score":0.5670632719993591},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5186564326286316},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4628227651119232},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4557071328163147},{"id":"https://openalex.org/keywords/singular-solution","display_name":"Singular solution","score":0.4271318316459656},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.41892579197883606},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33023449778556824},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.20005124807357788},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.18865394592285156},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.062247902154922485}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8777150511741638},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.7891544103622437},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.657253623008728},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.6347208619117737},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.595007061958313},{"id":"https://openalex.org/C114609681","wikidata":"https://www.wikidata.org/wiki/Q24839227","display_name":"Orthogonal collocation","level":5,"score":0.5670632719993591},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5186564326286316},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4628227651119232},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4557071328163147},{"id":"https://openalex.org/C135909967","wikidata":"https://www.wikidata.org/wiki/Q4338245","display_name":"Singular solution","level":2,"score":0.4271318316459656},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.41892579197883606},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33023449778556824},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.20005124807357788},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.18865394592285156},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.062247902154922485},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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:10.1080/00207160802123417","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160802123417","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1965386465","https://openalex.org/W1970439845","https://openalex.org/W1976349149","https://openalex.org/W1978142553","https://openalex.org/W2012163315","https://openalex.org/W2013984730","https://openalex.org/W2034617954","https://openalex.org/W2036064357","https://openalex.org/W2067027858","https://openalex.org/W2082677022","https://openalex.org/W2112390231"],"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/W2384941625","https://openalex.org/W2060099884"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"analyse":[4],"the":[5,10,24,43,46],"iterated":[6,47],"collocation":[7,48],"method":[8,49],"for":[9,50],"nonlinear":[11],"Urysohn":[12,51],"operator":[13],"equation":[14],"x=y+K(x)":[15],"with":[16],"K":[17],"a":[18],"singular":[19],"kernel.":[20],"The":[21],"paper":[22],"extends":[23],"study":[25],"[H.":[26],"Kaneko,":[27],"R.D.":[28],"Noren,":[29],"and":[30],"P.A.":[31],"Padilla,":[32],"J.":[33],"Comput.":[34],"Appl.":[35],"Math.":[36],"80":[37],"(1997),":[38],"pp.":[39],"335\u2013349]":[40],"in":[41],"which":[42],"convergence":[44],"of":[45],"equations":[52],"is":[53],"considered.":[54]},"counts_by_year":[{"year":2021,"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"}