{"id":"https://openalex.org/W2132916698","doi":"https://doi.org/10.1080/00207160701210646","title":"Fourth-order two-step iterative methods for determining multiple zeros of non-linear equations","display_name":"Fourth-order two-step iterative methods for determining multiple zeros of non-linear equations","publication_year":2007,"publication_date":"2007-07-01","ids":{"openalex":"https://openalex.org/W2132916698","doi":"https://doi.org/10.1080/00207160701210646","mag":"2132916698"},"language":"en","primary_location":{"id":"doi:10.1080/00207160701210646","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160701210646","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/A5102024596","display_name":"Nazir Ahmad Mir","orcid":"https://orcid.org/0000-0003-4209-6090"},"institutions":[{"id":"https://openalex.org/I16076960","display_name":"COMSATS University Islamabad","ror":"https://ror.org/00nqqvk19","country_code":"PK","type":"education","lineage":["https://openalex.org/I16076960"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"N. A. Mir","raw_affiliation_strings":["a   Department of Mathematics , COMSATS Institute of Information Technology , Plot No. 30, Sector H-8/1, Islamabad, 44000,  Pakistan","Department of Mathematics , COMSATS Institute of Information Technology , Plot No. 30, Sector H-8/1, Islamabad, 44000, Pakistan"],"affiliations":[{"raw_affiliation_string":"a   Department of Mathematics , COMSATS Institute of Information Technology , Plot No. 30, Sector H-8/1, Islamabad, 44000,  Pakistan","institution_ids":["https://openalex.org/I16076960"]},{"raw_affiliation_string":"Department of Mathematics , COMSATS Institute of Information Technology , Plot No. 30, Sector H-8/1, Islamabad, 44000, Pakistan","institution_ids":["https://openalex.org/I16076960"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078211416","display_name":"Naila Rafiq","orcid":null},"institutions":[{"id":"https://openalex.org/I4210141105","display_name":"Centre of Excellence in Molecular Biology","ror":"https://ror.org/03qfdvc46","country_code":"PK","type":"education","lineage":["https://openalex.org/I4210141105"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Naila Rafiq","raw_affiliation_strings":["b  Centre for Advanced Studies in Pure and Applied Mathematics, B. Z. University , Multan, 60800,  Pakistan","Centre for Advanced Studies in Pure and Applied Mathematics, B. Z. University , Multan, 60800, Pakistan"],"affiliations":[{"raw_affiliation_string":"b  Centre for Advanced Studies in Pure and Applied Mathematics, B. Z. University , Multan, 60800,  Pakistan","institution_ids":[]},{"raw_affiliation_string":"Centre for Advanced Studies in Pure and Applied Mathematics, B. Z. University , Multan, 60800, Pakistan","institution_ids":["https://openalex.org/I4210141105"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5102024596"],"corresponding_institution_ids":["https://openalex.org/I16076960"],"apc_list":null,"apc_paid":null,"fwci":0.5003,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.69612069,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"84","issue":"7","first_page":"971","last_page":"977"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","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/T12661","display_name":"Iterative Methods for Nonlinear Equations","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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9926999807357788,"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/mathematics","display_name":"Mathematics","score":0.8323040008544922},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.6196250319480896},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.5986206531524658},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5958049297332764},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5799022912979126},{"id":"https://openalex.org/keywords/linear-equation","display_name":"Linear equation","score":0.4797824025154114},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.47837844491004944},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.47607770562171936},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.46435049176216125},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.456265926361084},{"id":"https://openalex.org/keywords/local-convergence","display_name":"Local convergence","score":0.4339678883552551},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.42178019881248474},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.41446298360824585},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.36560797691345215},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2779531478881836},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.27238863706588745},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11656102538108826}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8323040008544922},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.6196250319480896},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5986206531524658},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5958049297332764},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5799022912979126},{"id":"https://openalex.org/C77346573","wikidata":"https://www.wikidata.org/wiki/Q484637","display_name":"Linear equation","level":2,"score":0.4797824025154114},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.47837844491004944},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.47607770562171936},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.46435049176216125},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.456265926361084},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.4339678883552551},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.42178019881248474},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.41446298360824585},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.36560797691345215},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2779531478881836},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27238863706588745},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11656102538108826},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160701210646","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160701210646","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":14,"referenced_works":["https://openalex.org/W1964170706","https://openalex.org/W1978149445","https://openalex.org/W1989513313","https://openalex.org/W1992709107","https://openalex.org/W1995365180","https://openalex.org/W2002635727","https://openalex.org/W2035380993","https://openalex.org/W2041102744","https://openalex.org/W2054082264","https://openalex.org/W2081263157","https://openalex.org/W2161462341","https://openalex.org/W2199004907","https://openalex.org/W2898916015","https://openalex.org/W3009644516"],"related_works":["https://openalex.org/W2378562963","https://openalex.org/W2350788688","https://openalex.org/W2353579944","https://openalex.org/W2103912232","https://openalex.org/W2089967807","https://openalex.org/W2588958454","https://openalex.org/W2031390949","https://openalex.org/W2078306205","https://openalex.org/W2351377961","https://openalex.org/W2170408898"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"describe":[4],"and":[5],"analyse":[6],"two":[7],"two-step":[8,39],"iterative":[9],"methods":[10,22,27],"for":[11],"finding":[12,42],"multiple":[13,30,40],"zeros":[14,31],"of":[15,54],"non-linear":[16],"equations.":[17],"We":[18],"prove":[19],"that":[20],"the":[21,29,37,52],"have":[23],"fourth-order":[24],"convergence.":[25],"The":[26,44],"calculate":[28],"with":[32],"high":[33],"accuracy.":[34],"These":[35],"are":[36],"first":[38],"zero":[41],"methods.":[43],"numerical":[45],"tests":[46],"show":[47],"their":[48],"better":[49],"performance":[50],"in":[51],"case":[53],"algebraic":[55],"as":[56,58],"well":[57],"non-algebraic":[59],"equations":[60]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
