{"id":"https://openalex.org/W4402989765","doi":"https://doi.org/10.3390/axioms13100675","title":"A Robust and Optimal Iterative Algorithm Employing a Weight Function for Solving Nonlinear Equations with Dynamics and Applications","display_name":"A Robust and Optimal Iterative Algorithm Employing a Weight Function for Solving Nonlinear Equations with Dynamics and Applications","publication_year":2024,"publication_date":"2024-09-30","ids":{"openalex":"https://openalex.org/W4402989765","doi":"https://doi.org/10.3390/axioms13100675"},"language":"en","primary_location":{"id":"doi:10.3390/axioms13100675","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13100675","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/axioms13100675","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004170119","display_name":"Shahid Abdullah","orcid":"https://orcid.org/0009-0002-8999-9406"},"institutions":[{"id":"https://openalex.org/I464993","display_name":"Barkatullah University","ror":"https://ror.org/02ax13658","country_code":"IN","type":"education","lineage":["https://openalex.org/I464993"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Shahid Abdullah","raw_affiliation_strings":["School of Advanced Sciences and Languages, VIT Bhopal University, Kothri-Kalan, Sehore 466114, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Advanced Sciences and Languages, VIT Bhopal University, Kothri-Kalan, Sehore 466114, India","institution_ids":["https://openalex.org/I464993"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023504039","display_name":"Neha Choubey","orcid":"https://orcid.org/0000-0002-6349-4904"},"institutions":[{"id":"https://openalex.org/I464993","display_name":"Barkatullah University","ror":"https://ror.org/02ax13658","country_code":"IN","type":"education","lineage":["https://openalex.org/I464993"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Neha Choubey","raw_affiliation_strings":["School of Advanced Sciences and Languages, VIT Bhopal University, Kothri-Kalan, Sehore 466114, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Advanced Sciences and Languages, VIT Bhopal University, Kothri-Kalan, Sehore 466114, India","institution_ids":["https://openalex.org/I464993"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066706220","display_name":"Suresh Dara","orcid":"https://orcid.org/0000-0002-1207-5208"},"institutions":[{"id":"https://openalex.org/I464993","display_name":"Barkatullah University","ror":"https://ror.org/02ax13658","country_code":"IN","type":"education","lineage":["https://openalex.org/I464993"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Suresh Dara","raw_affiliation_strings":["School of Advanced Sciences and Languages, VIT Bhopal University, Kothri-Kalan, Sehore 466114, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Advanced Sciences and Languages, VIT Bhopal University, Kothri-Kalan, Sehore 466114, India","institution_ids":["https://openalex.org/I464993"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079820359","display_name":"Moin\u2010ud\u2010Din Junjua","orcid":"https://orcid.org/0000-0002-1251-1532"},"institutions":[{"id":"https://openalex.org/I135237710","display_name":"Zhejiang Normal University","ror":"https://ror.org/01vevwk45","country_code":"CN","type":"education","lineage":["https://openalex.org/I135237710"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Moin-ud-Din Junjua","raw_affiliation_strings":["School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China"],"raw_orcid":"https://orcid.org/0000-0002-1251-1532","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China","institution_ids":["https://openalex.org/I135237710"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109555347","display_name":"T.A. Abdullah","orcid":null},"institutions":[{"id":"https://openalex.org/I8778637","display_name":"National Institute of Technology Srinagar","ror":"https://ror.org/03sfwvw54","country_code":"IN","type":"education","lineage":["https://openalex.org/I4210152752","https://openalex.org/I8778637"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Tawseef Abdullah","raw_affiliation_strings":["Department of Mechanical Engineering, National Institute of Technology, Hazratbal, Srinagar 190006, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, National Institute of Technology, Hazratbal, Srinagar 190006, India","institution_ids":["https://openalex.org/I8778637"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5004170119","https://openalex.org/A5079820359"],"corresponding_institution_ids":["https://openalex.org/I135237710","https://openalex.org/I464993"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":3.3689,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.92779177,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":98},"biblio":{"volume":"13","issue":"10","first_page":"675","last_page":"675"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9976999759674072,"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":0.9871000051498413,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6954489350318909},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.5916584730148315},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.49925851821899414},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.499159574508667},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.47760009765625},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4373522102832794},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.43444934487342834},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4092687666416168},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3546740412712097},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08550906181335449}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6954489350318909},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.5916584730148315},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49925851821899414},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.499159574508667},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.47760009765625},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4373522102832794},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.43444934487342834},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4092687666416168},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3546740412712097},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08550906181335449},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms13100675","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13100675","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:0abd1024d92f4595973ad06d3fc9a626","is_oa":true,"landing_page_url":"https://doaj.org/article/0abd1024d92f4595973ad06d3fc9a626","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 13, Iss 10, p 675 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms13100675","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13100675","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W1972417972","https://openalex.org/W1986527778","https://openalex.org/W2002108685","https://openalex.org/W2026376036","https://openalex.org/W2049193681","https://openalex.org/W2052199958","https://openalex.org/W2055308255","https://openalex.org/W2068000066","https://openalex.org/W2089373101","https://openalex.org/W2099981000","https://openalex.org/W2157719531","https://openalex.org/W2158308038","https://openalex.org/W2165754740","https://openalex.org/W2279247834","https://openalex.org/W2515866281","https://openalex.org/W2767146706","https://openalex.org/W2782299130","https://openalex.org/W2903124382","https://openalex.org/W2907186097","https://openalex.org/W2921216878","https://openalex.org/W2944321143","https://openalex.org/W3083297350","https://openalex.org/W3213255932","https://openalex.org/W4248241950","https://openalex.org/W4288441838","https://openalex.org/W4292451975","https://openalex.org/W4353062102","https://openalex.org/W4376959394","https://openalex.org/W4385553012","https://openalex.org/W4389200778","https://openalex.org/W4389542333","https://openalex.org/W4396720063","https://openalex.org/W4398205915","https://openalex.org/W6635339388","https://openalex.org/W6667713290","https://openalex.org/W6683331151","https://openalex.org/W6684473933","https://openalex.org/W6695277579"],"related_works":["https://openalex.org/W2154204858","https://openalex.org/W3209622820","https://openalex.org/W1636325709","https://openalex.org/W2724817865","https://openalex.org/W2400992695","https://openalex.org/W2382250648","https://openalex.org/W2382944939","https://openalex.org/W2367363545","https://openalex.org/W2586383879","https://openalex.org/W2067895158"],"abstract_inverted_index":{"This":[0],"study":[1,102],"introduces":[2,117],"a":[3,74,118,132,148,159],"novel,":[4],"iterative":[5,169],"algorithm":[6,69],"that":[7,89,179,189],"achieves":[8,22],"fourth-order":[9,49],"convergence":[10,42,109],"for":[11,61,143],"solving":[12],"nonlinear":[13],"equations.":[14],"Satisfying":[15],"the":[16,19,47,53,84,106,123,137,164,172],"Kung\u2013Traub":[17],"conjecture,":[18],"proposed":[20,68,107,181],"technique":[21],"an":[23,29,129],"optimal":[24,48],"order":[25],"of":[26,33,41,76,97,125,131,140,162,168,174,176,186],"four":[27],"with":[28],"efficiency":[30,165],"index":[31],"(I)":[32],"1.587,":[34],"requiring":[35],"three":[36],"function":[37],"evaluations.":[38],"An":[39],"analysis":[40,173],"is":[43,70,81],"presented":[44,60],"to":[45,145],"show":[46],"convergence.":[50,191],"To":[51],"verify":[52],"theoretical":[54],"results,":[55],"in-depth":[56],"numerical":[57],"comparisons":[58],"are":[59],"both":[62,163],"real":[63],"and":[64,79,86,99,113,150,166],"complex":[65],"domains.":[66],"The":[67,101],"specifically":[71],"examined":[72],"on":[73],"variety":[75],"polynomial":[77],"functions,":[78],"it":[80,90],"shown":[82],"by":[83,121],"efficient":[85],"accurate":[87],"results":[88],"outperforms":[91],"many":[92],"existing":[93],"algorithms":[94],"in":[95,154],"terms":[96],"speed":[98,167],"accuracy.":[100],"not":[103],"only":[104],"explores":[105],"method\u2019s":[108,133],"properties,":[110],"computational":[111],"efficiency,":[112],"stability":[114],"but":[115],"also":[116],"novel":[119],"perspective":[120],"considering":[122],"count":[124],"black":[126],"points":[127,188],"as":[128],"indicator":[130],"divergence.":[134],"By":[135],"analyzing":[136],"mean":[138],"number":[139],"iterations":[141],"necessary":[142],"methods":[144],"converge":[146],"within":[147],"cycle":[149],"measuring":[151],"CPU":[152],"time":[153],"seconds,":[155],"this":[156],"research":[157],"provides":[158],"holistic":[160],"assessment":[161],"methods.":[170],"Notably,":[171],"basins":[175],"attraction":[177],"illustrates":[178],"our":[180],"method":[182],"has":[183],"larger":[184],"sets":[185],"initial":[187],"yield":[190]},"counts_by_year":[{"year":2025,"cited_by_count":5}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
