{"id":"https://openalex.org/W2591242032","doi":"https://doi.org/10.1080/00207160.2017.1294687","title":"Discrete Legendre spectral Galerkin method for Urysohn integral equations","display_name":"Discrete Legendre spectral Galerkin method for Urysohn integral equations","publication_year":2017,"publication_date":"2017-02-24","ids":{"openalex":"https://openalex.org/W2591242032","doi":"https://doi.org/10.1080/00207160.2017.1294687","mag":"2591242032"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2017.1294687","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2017.1294687","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"],"host_organization_lineage_names":["Taylor & Francis"],"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/A5015072287","display_name":"Payel Das","orcid":"https://orcid.org/0000-0002-3239-4222"},"institutions":[{"id":"https://openalex.org/I145894827","display_name":"Indian Institute of Technology Kharagpur","ror":"https://ror.org/03w5sq511","country_code":"IN","type":"education","lineage":["https://openalex.org/I145894827"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Payel Das","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Technology, Kharagpur, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology, Kharagpur, India","institution_ids":["https://openalex.org/I145894827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037217684","display_name":"Gnaneshwar Nelakanti","orcid":"https://orcid.org/0000-0002-5247-9696"},"institutions":[{"id":"https://openalex.org/I145894827","display_name":"Indian Institute of Technology Kharagpur","ror":"https://ror.org/03w5sq511","country_code":"IN","type":"education","lineage":["https://openalex.org/I145894827"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Gnaneshwar Nelakanti","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Technology, Kharagpur, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology, Kharagpur, India","institution_ids":["https://openalex.org/I145894827"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087519125","display_name":"Guangqing Long","orcid":"https://orcid.org/0000-0002-0039-8974"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Guangqing Long","raw_affiliation_strings":["Department of Mathematics, GuangXi Teachers Education University, Nanning, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, GuangXi Teachers Education University, Nanning, People's Republic of China","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5015072287"],"corresponding_institution_ids":["https://openalex.org/I145894827"],"apc_list":null,"apc_paid":null,"fwci":0.154,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.43604975,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"95","issue":"3","first_page":"465","last_page":"489"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8920773267745972},{"id":"https://openalex.org/keywords/legendre-polynomials","display_name":"Legendre polynomials","score":0.8334858417510986},{"id":"https://openalex.org/keywords/superconvergence","display_name":"Superconvergence","score":0.7639580368995667},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.7000027298927307},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.5814629793167114},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5625858306884766},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.5515612363815308},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.5475063323974609},{"id":"https://openalex.org/keywords/spectral-method","display_name":"Spectral method","score":0.5293577313423157},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5198029279708862},{"id":"https://openalex.org/keywords/legendres-equation","display_name":"Legendre's equation","score":0.5053908824920654},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4717077910900116},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.4436757564544678},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.42685720324516296},{"id":"https://openalex.org/keywords/gaussian-quadrature","display_name":"Gaussian quadrature","score":0.4162614941596985},{"id":"https://openalex.org/keywords/nystr\u00f6m-method","display_name":"Nystr\u00f6m method","score":0.32956451177597046},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.13882294297218323},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.11947694420814514}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8920773267745972},{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.8334858417510986},{"id":"https://openalex.org/C83295009","wikidata":"https://www.wikidata.org/wiki/Q7643190","display_name":"Superconvergence","level":3,"score":0.7639580368995667},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.7000027298927307},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.5814629793167114},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5625858306884766},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.5515612363815308},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.5475063323974609},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.5293577313423157},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5198029279708862},{"id":"https://openalex.org/C86287605","wikidata":"https://www.wikidata.org/wiki/Q4454970","display_name":"Legendre's equation","level":3,"score":0.5053908824920654},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4717077910900116},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4436757564544678},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.42685720324516296},{"id":"https://openalex.org/C167196314","wikidata":"https://www.wikidata.org/wiki/Q767680","display_name":"Gaussian quadrature","level":4,"score":0.4162614941596985},{"id":"https://openalex.org/C48265008","wikidata":"https://www.wikidata.org/wiki/Q7071295","display_name":"Nystr\u00f6m method","level":3,"score":0.32956451177597046},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.13882294297218323},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11947694420814514},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"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/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2017.1294687","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2017.1294687","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"],"host_organization_lineage_names":["Taylor & Francis"],"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":[{"id":"https://openalex.org/G4610091474","display_name":null,"funder_award_id":"ZD2014080","funder_id":"https://openalex.org/F4320322768","funder_display_name":"Natural Science Foundation of Guangxi Province"},{"id":"https://openalex.org/G752429902","display_name":null,"funder_award_id":"11461011","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322768","display_name":"Natural Science Foundation of Guangxi Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W106404678","https://openalex.org/W205381016","https://openalex.org/W614581382","https://openalex.org/W648302553","https://openalex.org/W1978142553","https://openalex.org/W1982949943","https://openalex.org/W1985571217","https://openalex.org/W1998258828","https://openalex.org/W2000855689","https://openalex.org/W2001794693","https://openalex.org/W2006549404","https://openalex.org/W2077412880","https://openalex.org/W2084686777","https://openalex.org/W2117886479","https://openalex.org/W2130655033","https://openalex.org/W2151640244","https://openalex.org/W2168404272","https://openalex.org/W4230104359"],"related_works":["https://openalex.org/W2094577950","https://openalex.org/W2031157121","https://openalex.org/W1565666028","https://openalex.org/W2891538916","https://openalex.org/W4205354206","https://openalex.org/W2113328631","https://openalex.org/W2004690362","https://openalex.org/W3159111101","https://openalex.org/W4242964669","https://openalex.org/W4230612901"],"abstract_inverted_index":{"In":[0,44],"this":[1],"paper,":[2],"we":[3,46],"consider":[4],"the":[5,13,25,32,38,51,60,64,73],"discrete":[6,74],"Legendre":[7,66],"spectral":[8,67],"Galerkin":[9,68],"method":[10,69],"to":[11,31],"approximate":[12,26,29],"solution":[14,34],"of":[15,24,40,55,58],"Urysohn":[16],"integral":[17],"equation":[18],"with":[19],"smooth":[20],"kernel.":[21],"The":[22],"convergence":[23,41],"and":[27,37],"iterated":[28,65],"solutions":[30],"actual":[33],"is":[35,54],"discussed":[36],"rates":[39,62],"are":[42,70],"obtained.":[43],"particular":[45],"have":[47],"shown":[48],"that,":[49],"when":[50],"quadrature":[52],"rule":[53],"certain":[56],"degree":[57],"precision,":[59],"superconvergence":[61],"for":[63],"maintained":[71],"in":[72],"case.":[75]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}