{"id":"https://openalex.org/W4396237656","doi":"https://doi.org/10.1002/num.23105","title":"Generalized log orthogonal functions spectral collocation method for two dimensional weakly singular Volterra integral equations of the second kind","display_name":"Generalized log orthogonal functions spectral collocation method for two dimensional weakly singular Volterra integral equations of the second kind","publication_year":2024,"publication_date":"2024-04-29","ids":{"openalex":"https://openalex.org/W4396237656","doi":"https://doi.org/10.1002/num.23105"},"language":"en","primary_location":{"id":"doi:10.1002/num.23105","doi":"https://doi.org/10.1002/num.23105","is_oa":false,"landing_page_url":"https://doi.org/10.1002/num.23105","pdf_url":null,"source":{"id":"https://openalex.org/S19633754","display_name":"Numerical Methods for Partial Differential Equations","issn_l":"0749-159X","issn":["0749-159X","1098-2426"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-1","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Methods for Partial Differential Equations","raw_type":"journal-article"},"parent_works":[],"lineage":["https://openalex.org/W4396237656"],"child_works_count":0,"type":"article","is_traditional":true,"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/A5063177269","display_name":"Qiumei Huang","orcid":"https://orcid.org/0000-0002-5287-2009","observed_orcids":["https://orcid.org/0000-0002-5287-2009"]},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qiumei Huang","raw_affiliation_strings":["School of Mathematics, Statistics and Mechanics Beijing University of Technology  Beijing People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Statistics and Mechanics Beijing University of Technology  Beijing People's Republic of China","institution_ids":["https://openalex.org/I37796252"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100340998","display_name":"Min Wang","orcid":"https://orcid.org/0009-0008-0045-181X","observed_orcids":["https://orcid.org/0009-0008-0045-181X"]},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]},{"id":"https://openalex.org/I4210139958","display_name":"Beijing Computational Science Research Center","ror":"https://ror.org/04tavf782","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210139958"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Min Wang","raw_affiliation_strings":["Beijing Computational Science Research Center  Beijing People's Republic of China","School of Mathematics, Statistics and Mechanics Beijing University of Technology  Beijing People's Republic of China"],"raw_orcid":"https://orcid.org/0009-0008-0045-181X","affiliations":[{"raw_affiliation_string":"Beijing Computational Science Research Center  Beijing People's Republic of China","institution_ids":["https://openalex.org/I4210139958"]},{"raw_affiliation_string":"School of Mathematics, Statistics and Mechanics Beijing University of Technology  Beijing People's Republic of China","institution_ids":["https://openalex.org/I37796252"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100340998"],"corresponding_institution_ids":["https://openalex.org/I37796252","https://openalex.org/I4210139958"],"apc_list":{"value":3570,"currency":"USD","value_usd":3570},"apc_paid":null,"fwci":1.5564,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.77897702,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":97},"biblio":{"volume":"40","issue":"5","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.47920000553131104,"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"}},"topics":[{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.47920000553131104,"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"}},{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.2750999927520752,"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"}},{"id":"https://openalex.org/T11416","display_name":"Numerical Solvers for Ordinary Differential Equations","score":0.11990000307559967,"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/pseudospectral-method","display_name":"pseudospectral method","score":0.9710000157356262},{"id":"https://openalex.org/keywords/two-dimensional-integral-equations","display_name":"two-dimensional integral equations","score":0.8920000195503235},{"id":"https://openalex.org/keywords/endpoint-singularities","display_name":"endpoint singularities","score":0.7639999985694885},{"id":"https://openalex.org/keywords/convergence-analysis","display_name":"convergence analysis","score":0.7379999756813049},{"id":"https://openalex.org/keywords/numerical-solution-of-integral-equations","display_name":"numerical solution of integral equations","score":0.6899999976158142}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.867913544178009},{"id":"https://openalex.org/C21965488","wikidata":"https://www.wikidata.org/wiki/Q2632613","display_name":"Volterra integral equation","level":3,"score":0.740353524684906},{"id":"https://openalex.org/C92571104","wikidata":"https://www.wikidata.org/wiki/Q888122","display_name":"Singular integral","level":3,"score":0.5935993790626526},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.5893169045448303},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.5823203325271606},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.581286609172821},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5774048566818237},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.5378789901733398},{"id":"https://openalex.org/C167196314","wikidata":"https://www.wikidata.org/wiki/Q767680","display_name":"Gaussian quadrature","level":4,"score":0.5149334073066711},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4644154906272888},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.4300791025161743},{"id":"https://openalex.org/C114609681","wikidata":"https://www.wikidata.org/wiki/Q24839227","display_name":"Orthogonal collocation","level":5,"score":0.42572158575057983},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42526885867118835},{"id":"https://openalex.org/C48265008","wikidata":"https://www.wikidata.org/wiki/Q7071295","display_name":"Nystr\u00f6m method","level":3,"score":0.3022090494632721},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.10217899084091187},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.07142877578735352},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C62649853","wikidata":"https://www.wikidata.org/wiki/Q199687","display_name":"Remote sensing","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","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/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/num.23105","doi":"https://doi.org/10.1002/num.23105","is_oa":false,"landing_page_url":"https://doi.org/10.1002/num.23105","pdf_url":null,"source":{"id":"https://openalex.org/S19633754","display_name":"Numerical Methods for Partial Differential Equations","issn_l":"0749-159X","issn":["0749-159X","1098-2426"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-1","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Methods for Partial Differential Equations","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G4717361965","display_name":"\u79ef\u5206\u5fae\u5206\u65b9\u7a0b\u7684\u9ad8\u6548\u6570\u503c\u65b9\u6cd5\u7814\u7a76","funder_award_id":"11971047","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8297500790","display_name":null,"funder_award_id":"Z200002","funder_id":"https://openalex.org/F4320334977","funder_display_name":"Beijing Municipal Natural Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334977","display_name":"Beijing Municipal Natural Science Foundation","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1549220217","https://openalex.org/W1646339752","https://openalex.org/W1805381866","https://openalex.org/W1912930600","https://openalex.org/W1977486208","https://openalex.org/W1979762896","https://openalex.org/W1979950678","https://openalex.org/W1992415649","https://openalex.org/W1998424577","https://openalex.org/W2002983799","https://openalex.org/W2012144921","https://openalex.org/W2015622021","https://openalex.org/W2020988386","https://openalex.org/W2024169233","https://openalex.org/W2047244154","https://openalex.org/W2055212013","https://openalex.org/W2104506124","https://openalex.org/W2129883166","https://openalex.org/W2145736329","https://openalex.org/W2162080230","https://openalex.org/W2270749385","https://openalex.org/W2301264260","https://openalex.org/W2916289141","https://openalex.org/W2938553396","https://openalex.org/W3013039183","https://openalex.org/W3092227854","https://openalex.org/W3113526177","https://openalex.org/W3134415380","https://openalex.org/W4247375400","https://openalex.org/W4253937035","https://openalex.org/W4254630587","https://openalex.org/W4255636138","https://openalex.org/W4391232824"],"related_works":["https://openalex.org/W2301264260","https://openalex.org/W3092227854","https://openalex.org/W1992415649","https://openalex.org/W4410406188","https://openalex.org/W3000238978","https://openalex.org/W3093021240","https://openalex.org/W3216612220","https://openalex.org/W2946510029","https://openalex.org/W4391072573","https://openalex.org/W2901369572"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"article,":[3],"a":[4],"generalized":[5],"log":[6],"orthogonal":[7],"functions":[8],"(GLOFs)\u2010spectral":[9],"collocation":[10],"method":[11,49,82],"to":[12],"two":[13],"dimensional":[14],"weakly":[15,55],"singular":[16,56],"Volterra":[17,57],"integral":[18,58],"equations":[19,59],"of":[20,29,45,70,79],"the":[21,30,33,43,46,71,80],"second":[22],"kind":[23],"is":[24,64,74,83],"proposed.":[25],"The":[26,77],"mild":[27],"singularities":[28],"solution":[31,73],"at":[32],"interval":[34],"endpoint":[35],"can":[36],"be":[37],"captured":[38],"by":[39,85],"Gauss\u2010GLOFs":[40],"quadrature":[41],"and":[42],"shortcoming":[44],"traditional":[47],"spectral":[48],"which":[50],"cannot":[51],"well":[52],"deal":[53],"with":[54,60],"limited":[61],"regular":[62],"solutions":[63],"avoided.":[65],"A":[66],"detailed":[67],"convergence":[68],"analysis":[69],"numerical":[72,86],"carried":[75],"out.":[76],"efficiency":[78],"proposed":[81],"demonstrated":[84],"examples.":[87]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":2}],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2024-04-30T00:00:00"}
