{"id":"https://openalex.org/W4385411840","doi":"https://doi.org/10.1007/s11075-023-01629-3","title":"Singularity separation Chebyshev collocation method for weakly singular Volterra integral equations of the second kind","display_name":"Singularity separation Chebyshev collocation method for weakly singular Volterra integral equations of the second kind","publication_year":2023,"publication_date":"2023-08-01","ids":{"openalex":"https://openalex.org/W4385411840","doi":"https://doi.org/10.1007/s11075-023-01629-3"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-023-01629-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-023-01629-3","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","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/A5071032569","display_name":"Tongke Wang","orcid":"https://orcid.org/0000-0001-6694-0140"},"institutions":[{"id":"https://openalex.org/I15062923","display_name":"Tianjin Normal University","ror":"https://ror.org/05x2td559","country_code":"CN","type":"education","lineage":["https://openalex.org/I15062923"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Tongke Wang","raw_affiliation_strings":["School of Mathematical Sciences, Tianjin Normal University, Tianjin, 300387, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Tianjin Normal University, Tianjin, 300387, China","institution_ids":["https://openalex.org/I15062923"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060544481","display_name":"Huan Lian","orcid":"https://orcid.org/0000-0002-9141-350X"},"institutions":[{"id":"https://openalex.org/I15062923","display_name":"Tianjin Normal University","ror":"https://ror.org/05x2td559","country_code":"CN","type":"education","lineage":["https://openalex.org/I15062923"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huan Lian","raw_affiliation_strings":["School of Mathematical Sciences, Tianjin Normal University, Tianjin, 300387, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Tianjin Normal University, Tianjin, 300387, China","institution_ids":["https://openalex.org/I15062923"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100303347","display_name":"Lu Ji","orcid":null},"institutions":[{"id":"https://openalex.org/I15062923","display_name":"Tianjin Normal University","ror":"https://ror.org/05x2td559","country_code":"CN","type":"education","lineage":["https://openalex.org/I15062923"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lu Ji","raw_affiliation_strings":["School of Mathematical Sciences, Tianjin Normal University, Tianjin, 300387, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Tianjin Normal University, Tianjin, 300387, China","institution_ids":["https://openalex.org/I15062923"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5071032569"],"corresponding_institution_ids":["https://openalex.org/I15062923"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":1.8025,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.8377032,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"95","issue":"4","first_page":"1829","last_page":"1854"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":1.0,"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":1.0,"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":0.9994000196456909,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9986000061035156,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8357449769973755},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.6551908254623413},{"id":"https://openalex.org/keywords/volterra-integral-equation","display_name":"Volterra integral equation","score":0.6280325055122375},{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":0.5733287334442139},{"id":"https://openalex.org/keywords/chebyshev-equation","display_name":"Chebyshev equation","score":0.5720848441123962},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.5714560151100159},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.5362045168876648},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.531272292137146},{"id":"https://openalex.org/keywords/singular-integral","display_name":"Singular integral","score":0.5161188840866089},{"id":"https://openalex.org/keywords/chebyshev-iteration","display_name":"Chebyshev iteration","score":0.5063813924789429},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.48305636644363403},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.45564988255500793},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.4420994222164154},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.43623197078704834},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35515809059143066},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.20748808979988098},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.1398327350616455},{"id":"https://openalex.org/keywords/classical-orthogonal-polynomials","display_name":"Classical orthogonal polynomials","score":0.12106665968894958},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.06516587734222412},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.05238136649131775},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.051016420125961304}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8357449769973755},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.6551908254623413},{"id":"https://openalex.org/C21965488","wikidata":"https://www.wikidata.org/wiki/Q2632613","display_name":"Volterra integral equation","level":3,"score":0.6280325055122375},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.5733287334442139},{"id":"https://openalex.org/C142484921","wikidata":"https://www.wikidata.org/wiki/Q3890369","display_name":"Chebyshev equation","level":4,"score":0.5720848441123962},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.5714560151100159},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.5362045168876648},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.531272292137146},{"id":"https://openalex.org/C92571104","wikidata":"https://www.wikidata.org/wiki/Q888122","display_name":"Singular integral","level":3,"score":0.5161188840866089},{"id":"https://openalex.org/C196512905","wikidata":"https://www.wikidata.org/wiki/Q2457511","display_name":"Chebyshev iteration","level":3,"score":0.5063813924789429},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.48305636644363403},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.45564988255500793},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.4420994222164154},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.43623197078704834},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35515809059143066},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.20748808979988098},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.1398327350616455},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.12106665968894958},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.06516587734222412},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05238136649131775},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.051016420125961304},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11075-023-01629-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-023-01629-3","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8313573740","display_name":"\u754c\u9762PDE\u7ea6\u675f\u63a7\u5236\u95ee\u9898\u7684\u6709\u9650\u4f53\u79ef\u5143\u65b9\u6cd5\u53ca\u5176\u5728\u6570\u503c\u9884\u62a5\u4e2d\u7684\u5e94\u7528\u7814\u7a76","funder_award_id":"11971241","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"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":49,"referenced_works":["https://openalex.org/W1543326485","https://openalex.org/W1567668233","https://openalex.org/W1973020618","https://openalex.org/W1978958071","https://openalex.org/W1979950678","https://openalex.org/W1989439280","https://openalex.org/W1995027698","https://openalex.org/W1998424577","https://openalex.org/W1999030362","https://openalex.org/W2008114487","https://openalex.org/W2015085231","https://openalex.org/W2020988386","https://openalex.org/W2035685331","https://openalex.org/W2048805000","https://openalex.org/W2070438803","https://openalex.org/W2073732659","https://openalex.org/W2084148680","https://openalex.org/W2086023613","https://openalex.org/W2115120403","https://openalex.org/W2187264218","https://openalex.org/W2270749385","https://openalex.org/W2301264260","https://openalex.org/W2326052378","https://openalex.org/W2343077604","https://openalex.org/W2418110479","https://openalex.org/W2488968130","https://openalex.org/W2530116259","https://openalex.org/W2567196668","https://openalex.org/W2735173532","https://openalex.org/W2762055348","https://openalex.org/W2770674703","https://openalex.org/W2887451999","https://openalex.org/W2891804050","https://openalex.org/W2938553396","https://openalex.org/W2953364340","https://openalex.org/W2954462747","https://openalex.org/W2957985161","https://openalex.org/W2966373122","https://openalex.org/W2979937409","https://openalex.org/W2982303486","https://openalex.org/W2985775333","https://openalex.org/W3007625533","https://openalex.org/W3122055921","https://openalex.org/W3134415380","https://openalex.org/W4233879328","https://openalex.org/W4252219081","https://openalex.org/W4252371218","https://openalex.org/W4253937035","https://openalex.org/W4254246953"],"related_works":["https://openalex.org/W1585782015","https://openalex.org/W2136992695","https://openalex.org/W2979693432","https://openalex.org/W2135245226","https://openalex.org/W2136729106","https://openalex.org/W1980374758","https://openalex.org/W2037107080","https://openalex.org/W4385383347","https://openalex.org/W2159416289","https://openalex.org/W3048174355"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2026-07-16T13:24:37.021932","created_date":"2025-10-10T00:00:00"}
