{"id":"https://openalex.org/W4389620350","doi":"https://doi.org/10.1142/s0218127423501766","title":"An Optimal Eighth-Order One-Parameter Single-Root Finder: Chaotic Dynamics and Stability Analysis","display_name":"An Optimal Eighth-Order One-Parameter Single-Root Finder: Chaotic Dynamics and Stability Analysis","publication_year":2023,"publication_date":"2023-12-11","ids":{"openalex":"https://openalex.org/W4389620350","doi":"https://doi.org/10.1142/s0218127423501766"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127423501766","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1142/s0218127423501766","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","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/A5102005028","display_name":"Wenshuo Li","orcid":"https://orcid.org/0000-0003-2389-8311"},"institutions":[{"id":"https://openalex.org/I97009856","display_name":"Bohai University","ror":"https://ror.org/01kdzej58","country_code":"CN","type":"education","lineage":["https://openalex.org/I97009856"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenshuo Li","raw_affiliation_strings":["School of Mathematical Sciences, Bohai University, New Songshan District, Jinzhou City, Liaoning Province, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Bohai University, New Songshan District, Jinzhou City, Liaoning Province, P. R. China","institution_ids":["https://openalex.org/I97009856"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024989917","display_name":"Xiaofeng Wang","orcid":"https://orcid.org/0000-0001-8524-6488"},"institutions":[{"id":"https://openalex.org/I97009856","display_name":"Bohai University","ror":"https://ror.org/01kdzej58","country_code":"CN","type":"education","lineage":["https://openalex.org/I97009856"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiaofeng Wang","raw_affiliation_strings":["School of Mathematical Sciences, Bohai University, New Songshan District, Jinzhou City, Liaoning Province, P. R. China"],"raw_orcid":"https://orcid.org/0000-0001-8524-6488","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Bohai University, New Songshan District, Jinzhou City, Liaoning Province, P. R. China","institution_ids":["https://openalex.org/I97009856"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5024989917"],"corresponding_institution_ids":["https://openalex.org/I97009856"],"apc_list":null,"apc_paid":null,"fwci":0.3633,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.56477215,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"33","issue":"15","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9998000264167786,"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":0.9998000264167786,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9785000085830688,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.9782000184059143,"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/iterative-method","display_name":"Iterative method","score":0.6754052639007568},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6508407592773438},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.6095175743103027},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5369467735290527},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.4885938763618469},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.4761483669281006},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4632934331893921},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4593660235404968},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.44990357756614685},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.42221567034721375},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.3972106873989105},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3508926033973694},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2468319833278656},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23390966653823853}],"concepts":[{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.6754052639007568},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6508407592773438},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.6095175743103027},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5369467735290527},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.4885938763618469},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.4761483669281006},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4632934331893921},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4593660235404968},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.44990357756614685},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.42221567034721375},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.3972106873989105},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3508926033973694},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2468319833278656},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23390966653823853},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127423501766","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1142/s0218127423501766","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.41999998688697815,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[{"id":"https://openalex.org/G3596841339","display_name":null,"funder_award_id":"61976027","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"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1841330889","https://openalex.org/W1996998378","https://openalex.org/W2047475327","https://openalex.org/W2048366372","https://openalex.org/W2062985118","https://openalex.org/W2067520338","https://openalex.org/W2078206416","https://openalex.org/W2091326168","https://openalex.org/W2116633858","https://openalex.org/W2137363905","https://openalex.org/W2141394518","https://openalex.org/W2197810208","https://openalex.org/W2320104866","https://openalex.org/W2562150112","https://openalex.org/W2588438036","https://openalex.org/W2743016060","https://openalex.org/W2944352255","https://openalex.org/W2984929756","https://openalex.org/W3020868773","https://openalex.org/W3037894255","https://openalex.org/W3085175920","https://openalex.org/W3138433766","https://openalex.org/W4237021800","https://openalex.org/W4248072974","https://openalex.org/W4307117562","https://openalex.org/W4313461378","https://openalex.org/W4321375138","https://openalex.org/W4385984837"],"related_works":["https://openalex.org/W2391540797","https://openalex.org/W4206623065","https://openalex.org/W2005355485","https://openalex.org/W1570727143","https://openalex.org/W168375694","https://openalex.org/W2703435152","https://openalex.org/W2119092717","https://openalex.org/W2063555990","https://openalex.org/W2002820797","https://openalex.org/W3153461053"],"abstract_inverted_index":{"In":[0,173],"this":[1,184,215,223],"paper,":[2],"we":[3,40,56,77,134],"focus":[4],"on":[5,111,169],"a":[6,79],"class":[7],"of":[8,61,82,88,97,148,156,166,196,222],"optimal":[9,36,43],"eighth-order":[10,44],"iterative":[11,26,38,46,67,90,185,192,216,224],"methods,":[12],"initially":[13],"proposed":[14],"by":[15,175,214],"Sharma":[16],"et":[17],"al.,":[18],"whose":[19],"second":[20],"step":[21],"can":[22,49,180],"choose":[23],"any":[24],"fourth-order":[25,37],"method.":[27,91,225],"By":[28],"selecting":[29],"the":[30,58,66,70,83,89,95,107,112,131,139,146,154,164,170,190,203,220],"first":[31],"two":[32],"steps":[33],"as":[34,118],"an":[35,42],"method,":[39,47,217],"derive":[41],"one-parameter":[45],"which":[48,218],"solve":[50],"nonlinear":[51,207,210],"systems.":[52],"Employing":[53],"fractal":[54],"theory,":[55],"investigate":[57],"dynamic":[59],"behavior":[60],"rational":[62],"operators":[63],"associated":[64],"with":[65,115],"method":[68,186,193],"through":[69],"Scaling":[71],"theorem":[72],"and":[73,86,101,106,143,199,209],"M\u00f6bius":[74],"transformation.":[75],"Subsequently,":[76],"conduct":[78],"comprehensive":[80],"study":[81],"chaotic":[84],"dynamics":[85],"stability":[87],"Our":[92],"analysis":[93],"involves":[94],"examination":[96],"strange":[98],"fixed":[99],"points":[100,117],"their":[102],"stability,":[103],"critical":[104,116],"points,":[105],"parameter":[108,128,141,150,158,167],"spaces":[109],"generated":[110],"complex":[113],"plane":[114],"initial":[119],"points.":[120],"We":[121],"utilize":[122],"these":[123],"findings":[124],"to":[125,189],"intuitively":[126],"select":[127],"values":[129,142],"from":[130],"figures.":[132],"Furthermore,":[133],"generate":[135],"dynamical":[136],"planes":[137],"for":[138],"selected":[140],"ultimately":[144],"determine":[145],"range":[147,155],"unstable":[149],"values,":[151],"thus":[152],"obtaining":[153],"stable":[157],"values.":[159],"The":[160],"bifurcation":[161],"diagram":[162],"shows":[163,219],"influence":[165],"selection":[168],"iteration":[171],"sequence.":[172],"addition,":[174],"drawing":[176],"attractive":[177],"basins,":[178],"it":[179],"be":[181],"seen":[182],"that":[183],"is":[187],"superior":[188],"same-order":[191],"in":[194],"terms":[195],"convergence":[197],"speed":[198],"average":[200],"iterations.":[201],"Finally,":[202],"matrix":[204],"sign":[205],"function,":[206],"equation":[208],"system":[211],"are":[212],"solved":[213],"applicability":[221]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}