{"id":"https://openalex.org/W3006667252","doi":"https://doi.org/10.1007/s40314-020-1100-5","title":"Galerkin and multi-Galerkin methods for weakly singular Volterra\u2013Hammerstein integral equations and their convergence analysis","display_name":"Galerkin and multi-Galerkin methods for weakly singular Volterra\u2013Hammerstein integral equations and their convergence analysis","publication_year":2020,"publication_date":"2020-02-10","ids":{"openalex":"https://openalex.org/W3006667252","doi":"https://doi.org/10.1007/s40314-020-1100-5","mag":"3006667252"},"language":"en","primary_location":{"id":"doi:10.1007/s40314-020-1100-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-020-1100-5","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"1807-0302","issn":["1807-0302","2238-3603"],"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":"Computational and Applied 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/A5052585288","display_name":"Kapil Kant","orcid":"https://orcid.org/0000-0001-6812-9167"},"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":"Kapil Kant","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, 721 302, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, 721 302, India","institution_ids":["https://openalex.org/I145894827"]}]},{"author_position":"last","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, Kharagpur, 721 302, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, 721 302, India","institution_ids":["https://openalex.org/I145894827"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5052585288"],"corresponding_institution_ids":["https://openalex.org/I145894827"],"apc_list":null,"apc_paid":null,"fwci":0.3503,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.66246812,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"39","issue":"2","first_page":null,"last_page":null},"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9995999932289124,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9988999962806702,"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/galerkin-method","display_name":"Galerkin method","score":0.8294064998626709},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8159346580505371},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.6673606634140015},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6486849784851074},{"id":"https://openalex.org/keywords/volterra-integral-equation","display_name":"Volterra integral equation","score":0.5398790836334229},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.5003104209899902},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.49982571601867676},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.4928765296936035},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.4709295332431793},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4682878851890564},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.439222514629364},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.42286232113838196},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.420958936214447},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40884941816329956},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.21562480926513672},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.17760738730430603},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.055447548627853394}],"concepts":[{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.8294064998626709},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8159346580505371},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.6673606634140015},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6486849784851074},{"id":"https://openalex.org/C21965488","wikidata":"https://www.wikidata.org/wiki/Q2632613","display_name":"Volterra integral equation","level":3,"score":0.5398790836334229},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.5003104209899902},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.49982571601867676},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.4928765296936035},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4709295332431793},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4682878851890564},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.439222514629364},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.42286232113838196},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.420958936214447},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40884941816329956},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.21562480926513672},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.17760738730430603},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.055447548627853394},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s40314-020-1100-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-020-1100-5","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"1807-0302","issn":["1807-0302","2238-3603"],"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":"Computational and Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6063733459","display_name":null,"funder_award_id":"02011/6/2019NBHM(R.P)/R & D II /1236 dated 28/1/2019","funder_id":"https://openalex.org/F4320323196","funder_display_name":"National Board for Higher Mathematics"}],"funders":[{"id":"https://openalex.org/F4320323196","display_name":"National Board for Higher Mathematics","ror":"https://ror.org/02m388s04"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W147405543","https://openalex.org/W614581382","https://openalex.org/W1964149437","https://openalex.org/W1965386465","https://openalex.org/W1965500773","https://openalex.org/W1979762896","https://openalex.org/W1979950678","https://openalex.org/W1981828637","https://openalex.org/W1998424577","https://openalex.org/W1999030362","https://openalex.org/W2002634869","https://openalex.org/W2008114487","https://openalex.org/W2020988386","https://openalex.org/W2038992763","https://openalex.org/W2044610770","https://openalex.org/W2050679275","https://openalex.org/W2057890001","https://openalex.org/W2084148680","https://openalex.org/W2090344516","https://openalex.org/W2090886631","https://openalex.org/W2094425535","https://openalex.org/W2144181355","https://openalex.org/W2192231559","https://openalex.org/W2269404167","https://openalex.org/W2293041380","https://openalex.org/W2408140492","https://openalex.org/W2480176609","https://openalex.org/W2585014300","https://openalex.org/W2893968173","https://openalex.org/W2910443655","https://openalex.org/W4252219081","https://openalex.org/W4252371218"],"related_works":["https://openalex.org/W2022639369","https://openalex.org/W2982093746","https://openalex.org/W2267613321","https://openalex.org/W3043435143","https://openalex.org/W2158006240","https://openalex.org/W2162026849","https://openalex.org/W1967648380","https://openalex.org/W2394687667","https://openalex.org/W4253848581","https://openalex.org/W1985051213"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}