{"id":"https://openalex.org/W4205943801","doi":"https://doi.org/10.1080/00207160.2022.2028778","title":"Error analysis of reiterated projection methods for Hammerstein integral equations","display_name":"Error analysis of reiterated projection methods for Hammerstein integral equations","publication_year":2022,"publication_date":"2022-01-12","ids":{"openalex":"https://openalex.org/W4205943801","doi":"https://doi.org/10.1080/00207160.2022.2028778"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2022.2028778","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2022.2028778","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/A5040887229","display_name":"Samiran Chakraborty","orcid":"https://orcid.org/0009-0003-3128-0199"},"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":"Samiran Chakraborty","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Technology, Kharagpur, India"],"raw_orcid":null,"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/A5052585288","display_name":"Kapil Kant","orcid":"https://orcid.org/0000-0001-6812-9167"},"institutions":[{"id":"https://openalex.org/I94234084","display_name":"Indian Institute of Technology Kanpur","ror":"https://ror.org/05pjsgx75","country_code":"IN","type":"education","lineage":["https://openalex.org/I94234084"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Kapil Kant","raw_affiliation_strings":["Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, India"],"raw_orcid":"https://orcid.org/0000-0001-6812-9167","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, India","institution_ids":["https://openalex.org/I94234084"]}]},{"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, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology, Kharagpur, India","institution_ids":["https://openalex.org/I145894827"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5052585288"],"corresponding_institution_ids":["https://openalex.org/I94234084"],"apc_list":null,"apc_paid":null,"fwci":0.411,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.51990802,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"99","issue":"10","first_page":"2001","last_page":"2017"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9986000061035156,"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/T10514","display_name":"Numerical methods in engineering","score":0.9979000091552734,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9032891392707825},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.7274121046066284},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5672746896743774},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5091885924339294},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.47021129727363586},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.4700925350189209},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.44492673873901367},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.42920905351638794},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3646240234375},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2692396640777588},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.2633315920829773}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9032891392707825},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.7274121046066284},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5672746896743774},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5091885924339294},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.47021129727363586},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.4700925350189209},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44492673873901367},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.42920905351638794},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3646240234375},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2692396640777588},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2633315920829773},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2022.2028778","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2022.2028778","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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W147405543","https://openalex.org/W169461701","https://openalex.org/W232674853","https://openalex.org/W614581382","https://openalex.org/W1966013041","https://openalex.org/W1969193723","https://openalex.org/W1970439845","https://openalex.org/W1974562296","https://openalex.org/W1976349149","https://openalex.org/W1978142553","https://openalex.org/W1985804948","https://openalex.org/W2012163315","https://openalex.org/W2014208709","https://openalex.org/W2034617954","https://openalex.org/W2036064357","https://openalex.org/W2036156558","https://openalex.org/W2040631649","https://openalex.org/W2044610770","https://openalex.org/W2050679275","https://openalex.org/W2056632561","https://openalex.org/W2067027858","https://openalex.org/W2073453289","https://openalex.org/W2084686777","https://openalex.org/W2094425535","https://openalex.org/W2104390620","https://openalex.org/W2269404167","https://openalex.org/W2504814367","https://openalex.org/W2584285487","https://openalex.org/W2597763973","https://openalex.org/W2799267564","https://openalex.org/W2910443655","https://openalex.org/W2954585071","https://openalex.org/W3108043981","https://openalex.org/W3124600136"],"related_works":["https://openalex.org/W2952185452","https://openalex.org/W2385263368","https://openalex.org/W2798106756","https://openalex.org/W2124287120","https://openalex.org/W2046736294","https://openalex.org/W2347422947","https://openalex.org/W1951249712","https://openalex.org/W2061292372","https://openalex.org/W2980815195","https://openalex.org/W2351235964"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,46,83],"consider":[4],"the":[5,20,59,65,74,77,86,91,97,110,115,121,137],"Newton-iteration":[6,61,93,117],"scheme":[7,62,94,118],"based":[8],"on":[9],"Galerkin":[10,53,87],"and":[11,26,30,54,68,104,127],"multi-Galerkin":[12,55,111],"operators":[13],"to":[14],"solve":[15],"non-linear":[16],"integral":[17],"equations":[18],"of":[19,39,43,76,139],"Fredholm-Hammerstein":[21],"type":[22,32],"for":[23,49,101,106,124,129,136],"both":[24],"smooth":[25,51],"weakly":[27,80],"singular":[28,81],"algebraic":[29,102,125],"logarithmic":[31,107,130],"kernels.":[33,108,131],"By":[34],"choosing":[35],"Xn":[36],"as":[37],"space":[38],"piecewise":[40],"polynomials":[41],"subspace":[42],"degree":[44],"\u2264r\u22121,":[45],"show":[47,84],"that":[48,85],"a":[50],"kernel,":[52],"approximate":[56,88,112],"solution":[57,89,113],"in":[58,90,114],"kth":[60,92,116],"converges":[63,95,119],"with":[64,96,120],"orders":[66,98,122],"O(h(k+1)r)":[67],"O(h(2k+3)r),":[69],"respectively,":[70],"where":[71],"h":[72],"is":[73],"norm":[75],"partition.":[78],"For":[79],"kernels,":[82],"O(hr+k(1\u2212\u03b1)),":[99],"0<\u03b1<1":[100],"kernels":[103,126],"O(hr+k(log\u2061h)k)":[105],"Also":[109],"O(hr+(k+1)(1\u2212\u03b1))":[123],"O(hr+k+1(log\u2061h)k+1)":[128],"Numerical":[132],"results":[133],"are":[134],"given":[135],"justification":[138],"our":[140],"theoretical":[141],"results.":[142]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
