{"id":"https://openalex.org/W2924092691","doi":"https://doi.org/10.1007/s11075-019-00693-y","title":"A posteriori error estimation for a singularly perturbed Volterra integro-differential equation","display_name":"A posteriori error estimation for a singularly perturbed Volterra integro-differential equation","publication_year":2019,"publication_date":"2019-03-26","ids":{"openalex":"https://openalex.org/W2924092691","doi":"https://doi.org/10.1007/s11075-019-00693-y","mag":"2924092691"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-019-00693-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-019-00693-y","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/A5063573580","display_name":"Jian Huang","orcid":"https://orcid.org/0000-0002-4730-244X"},"institutions":[{"id":"https://openalex.org/I1315279114","display_name":"Zhejiang Wanli University","ror":"https://ror.org/00rjdhd62","country_code":"CN","type":"education","lineage":["https://openalex.org/I1315279114"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jian Huang","raw_affiliation_strings":["Institute of Mathematics, Zhejiang Wanli University, Ningbo, 315100, Zhejiang, People\u2019s Republic of China","Institute of Mathematics, Zhejiang Wanli University, Ningbo, 315100, Zhejiang, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Zhejiang Wanli University, Ningbo, 315100, Zhejiang, People\u2019s Republic of China","institution_ids":["https://openalex.org/I1315279114"]},{"raw_affiliation_string":"Institute of Mathematics, Zhejiang Wanli University, Ningbo, 315100, Zhejiang, People's Republic of China","institution_ids":["https://openalex.org/I1315279114"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003721958","display_name":"Zhongdi Cen","orcid":"https://orcid.org/0000-0001-9739-2036"},"institutions":[{"id":"https://openalex.org/I1315279114","display_name":"Zhejiang Wanli University","ror":"https://ror.org/00rjdhd62","country_code":"CN","type":"education","lineage":["https://openalex.org/I1315279114"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhongdi Cen","raw_affiliation_strings":["Institute of Mathematics, Zhejiang Wanli University, Ningbo, 315100, Zhejiang, People\u2019s Republic of China","Institute of Mathematics, Zhejiang Wanli University, Ningbo, 315100, Zhejiang, People's Republic of China"],"raw_orcid":"https://orcid.org/0000-0001-9739-2036","affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Zhejiang Wanli University, Ningbo, 315100, Zhejiang, People\u2019s Republic of China","institution_ids":["https://openalex.org/I1315279114"]},{"raw_affiliation_string":"Institute of Mathematics, Zhejiang Wanli University, Ningbo, 315100, Zhejiang, People's Republic of China","institution_ids":["https://openalex.org/I1315279114"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100523812","display_name":"Aimin Xu","orcid":null},"institutions":[{"id":"https://openalex.org/I1315279114","display_name":"Zhejiang Wanli University","ror":"https://ror.org/00rjdhd62","country_code":"CN","type":"education","lineage":["https://openalex.org/I1315279114"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Aimin Xu","raw_affiliation_strings":["Institute of Mathematics, Zhejiang Wanli University, Ningbo, 315100, Zhejiang, People\u2019s Republic of China","Institute of Mathematics, Zhejiang Wanli University, Ningbo, 315100, Zhejiang, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Zhejiang Wanli University, Ningbo, 315100, Zhejiang, People\u2019s Republic of China","institution_ids":["https://openalex.org/I1315279114"]},{"raw_affiliation_string":"Institute of Mathematics, Zhejiang Wanli University, Ningbo, 315100, Zhejiang, People's Republic of China","institution_ids":["https://openalex.org/I1315279114"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102852831","display_name":"Li\u2010Bin Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I150807315","display_name":"Guangxi University","ror":"https://ror.org/02c9qn167","country_code":"CN","type":"education","lineage":["https://openalex.org/I150807315"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li-Bin Liu","raw_affiliation_strings":["School of Mathematics and Statistics, Guangxi Teachers Education University, Nanning, 530023, Guangxi, People\u2019s Republic of China","School of Mathematics and Statistics, Guangxi Teachers Education University, Nanning, 530023, Guangxi, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Guangxi Teachers Education University, Nanning, 530023, Guangxi, People\u2019s Republic of China","institution_ids":["https://openalex.org/I150807315"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Guangxi Teachers Education University, Nanning, 530023, Guangxi, People's Republic of China","institution_ids":["https://openalex.org/I150807315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5063573580"],"corresponding_institution_ids":["https://openalex.org/I1315279114"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":3.569,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.92916283,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"83","issue":"2","first_page":"549","last_page":"563"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":1.0,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9771999716758728,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9158999919891357,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8283367156982422},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.729770302772522},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.6195076704025269},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.599600076675415},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.5995586514472961},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.544224739074707},{"id":"https://openalex.org/keywords/sinc-function","display_name":"Sinc function","score":0.5177925825119019},{"id":"https://openalex.org/keywords/volterra-integral-equation","display_name":"Volterra integral equation","score":0.4711137115955353},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4686547815799713},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.42706021666526794},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.4077458381652832},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38400083780288696},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.13181009888648987}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8283367156982422},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.729770302772522},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.6195076704025269},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.599600076675415},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.5995586514472961},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.544224739074707},{"id":"https://openalex.org/C152303783","wikidata":"https://www.wikidata.org/wiki/Q855949","display_name":"Sinc function","level":2,"score":0.5177925825119019},{"id":"https://openalex.org/C21965488","wikidata":"https://www.wikidata.org/wiki/Q2632613","display_name":"Volterra integral equation","level":3,"score":0.4711137115955353},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4686547815799713},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.42706021666526794},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.4077458381652832},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38400083780288696},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.13181009888648987},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11075-019-00693-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-019-00693-y","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/G2071423880","display_name":null,"funder_award_id":"2018A10041","funder_id":"https://openalex.org/F4320335444","funder_display_name":"Soft Science Foundation of Ningbo"},{"id":"https://openalex.org/G3747971445","display_name":null,"funder_award_id":"11761015","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/F4320335444","display_name":"Soft Science Foundation of Ningbo","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W609598071","https://openalex.org/W1476132770","https://openalex.org/W1967786809","https://openalex.org/W1973297078","https://openalex.org/W1973656183","https://openalex.org/W1975670568","https://openalex.org/W1983495489","https://openalex.org/W1996536528","https://openalex.org/W2019223491","https://openalex.org/W2021036060","https://openalex.org/W2024354319","https://openalex.org/W2025443088","https://openalex.org/W2030209714","https://openalex.org/W2035159203","https://openalex.org/W2040513609","https://openalex.org/W2040599320","https://openalex.org/W2050511353","https://openalex.org/W2066626652","https://openalex.org/W2087297463","https://openalex.org/W2148887236","https://openalex.org/W2163017860","https://openalex.org/W2171902694","https://openalex.org/W2314863090","https://openalex.org/W2372292523","https://openalex.org/W2519419103","https://openalex.org/W4247953052","https://openalex.org/W4249149928"],"related_works":["https://openalex.org/W2517687681","https://openalex.org/W2118560105","https://openalex.org/W2387536758","https://openalex.org/W2358959122","https://openalex.org/W4401089097","https://openalex.org/W2189527329","https://openalex.org/W1997254107","https://openalex.org/W4225984655","https://openalex.org/W2031624200","https://openalex.org/W1539637428"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}