{"id":"https://openalex.org/W2525583675","doi":"https://doi.org/10.3390/a9040065","title":"Local Convergence Analysis of an Eighth Order Scheme Using Hypothesis Only on the First Derivative","display_name":"Local Convergence Analysis of an Eighth Order Scheme Using Hypothesis Only on the First Derivative","publication_year":2016,"publication_date":"2016-09-29","ids":{"openalex":"https://openalex.org/W2525583675","doi":"https://doi.org/10.3390/a9040065","mag":"2525583675"},"language":"en","primary_location":{"id":"doi:10.3390/a9040065","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a9040065","pdf_url":"https://www.mdpi.com/1999-4893/9/4/65/pdf?version=1475120624","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"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":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/9/4/65/pdf?version=1475120624","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087674067","display_name":"Ioannis K. Argyros","orcid":"https://orcid.org/0000-0002-9189-9298"},"institutions":[{"id":"https://openalex.org/I113618177","display_name":"Cameron University","ror":"https://ror.org/00rgv0036","country_code":"US","type":"education","lineage":["https://openalex.org/I113618177"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ioannis Argyros","raw_affiliation_strings":["Department of Mathematics Sciences Lawton, Cameron University, Lawton, OK 73505, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics Sciences Lawton, Cameron University, Lawton, OK 73505, USA","institution_ids":["https://openalex.org/I113618177"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078192871","display_name":"Ramandeep Behl","orcid":"https://orcid.org/0000-0003-1505-8945"},"institutions":[{"id":"https://openalex.org/I95023434","display_name":"University of KwaZulu-Natal","ror":"https://ror.org/04qzfn040","country_code":"ZA","type":"education","lineage":["https://openalex.org/I95023434"]}],"countries":["ZA"],"is_corresponding":true,"raw_author_name":"Ramandeep Behl","raw_affiliation_strings":["School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X01, Pietermaritzburg 3209, South Africa"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X01, Pietermaritzburg 3209, South Africa","institution_ids":["https://openalex.org/I95023434"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038746363","display_name":"S. S. Motsa","orcid":"https://orcid.org/0000-0002-3969-9598"},"institutions":[{"id":"https://openalex.org/I95023434","display_name":"University of KwaZulu-Natal","ror":"https://ror.org/04qzfn040","country_code":"ZA","type":"education","lineage":["https://openalex.org/I95023434"]}],"countries":["ZA"],"is_corresponding":false,"raw_author_name":"Sandile Motsa","raw_affiliation_strings":["School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X01, Pietermaritzburg 3209, South Africa"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X01, Pietermaritzburg 3209, South Africa","institution_ids":["https://openalex.org/I95023434"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5078192871"],"corresponding_institution_ids":["https://openalex.org/I95023434"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.4563,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.65597668,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"9","issue":"4","first_page":"65","last_page":"65"},"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":0.9933000206947327,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9739000201225281,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.7320970296859741},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6625992655754089},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6612334251403809},{"id":"https://openalex.org/keywords/taylor-series","display_name":"Taylor series","score":0.6247137188911438},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.6087762117385864},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5916177034378052},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5910977721214294},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5300737619400024},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5226980447769165},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.5186406970024109},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.499788761138916},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.464647501707077},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.4225446581840515},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.4222591817378998},{"id":"https://openalex.org/keywords/unconditional-convergence","display_name":"Unconditional convergence","score":0.4181234836578369},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33952921628952026},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3167768120765686},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.3138607442378998},{"id":"https://openalex.org/keywords/compact-convergence","display_name":"Compact convergence","score":0.28507915139198303},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23805788159370422}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7320970296859741},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6625992655754089},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6612334251403809},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.6247137188911438},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.6087762117385864},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5916177034378052},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5910977721214294},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5300737619400024},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5226980447769165},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.5186406970024109},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.499788761138916},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.464647501707077},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.4225446581840515},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.4222591817378998},{"id":"https://openalex.org/C89397928","wikidata":"https://www.wikidata.org/wiki/Q1630320","display_name":"Unconditional convergence","level":5,"score":0.4181234836578369},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33952921628952026},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3167768120765686},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.3138607442378998},{"id":"https://openalex.org/C5871375","wikidata":"https://www.wikidata.org/wiki/Q1780715","display_name":"Compact convergence","level":4,"score":0.28507915139198303},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23805788159370422},{"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/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/a9040065","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a9040065","pdf_url":"https://www.mdpi.com/1999-4893/9/4/65/pdf?version=1475120624","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"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":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:35dfb99812ba42a48887c6dbd2c75603","is_oa":true,"landing_page_url":"https://doaj.org/article/35dfb99812ba42a48887c6dbd2c75603","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 9, Iss 4, p 65 (2016)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1999-4893/9/4/65/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/a9040065","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms; Volume 9; Issue 4; Pages: 65","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/a9040065","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a9040065","pdf_url":"https://www.mdpi.com/1999-4893/9/4/65/pdf?version=1475120624","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"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":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2525583675.pdf","grobid_xml":"https://content.openalex.org/works/W2525583675.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W576148093","https://openalex.org/W1129295489","https://openalex.org/W1971939073","https://openalex.org/W1982301815","https://openalex.org/W1988627280","https://openalex.org/W2017317106","https://openalex.org/W2025159184","https://openalex.org/W2025716285","https://openalex.org/W2026119704","https://openalex.org/W2047475327","https://openalex.org/W2051457659","https://openalex.org/W2054711601","https://openalex.org/W2089145697","https://openalex.org/W2104500275","https://openalex.org/W4233832035"],"related_works":["https://openalex.org/W1652856812","https://openalex.org/W4247254407","https://openalex.org/W2055714564","https://openalex.org/W2023041386","https://openalex.org/W1484118303","https://openalex.org/W2347555707","https://openalex.org/W1989433389","https://openalex.org/W2063689210","https://openalex.org/W2010976053","https://openalex.org/W2360938646"],"abstract_inverted_index":{"In":[0,40,116],"this":[1,100,117,165],"paper,":[2],"we":[3,31,102,119],"propose":[4],"a":[5,17,22,26,134],"local":[6],"convergence":[7,57,131],"analysis":[8],"of":[9,21,37,56,75,83,125,136,153,167],"an":[10,41],"eighth":[11],"order":[12,55,70,91,114],"three-step":[13],"method":[14],"to":[15,67,112,149],"approximate":[16],"locally":[18],"unique":[19],"solution":[20],"nonlinear":[23,154],"equation":[24],"in":[25,94],"Banach":[27],"space":[28],"setting.":[29],"Further,":[30],"also":[32,129],"study":[33,161],"the":[34,54,68,76,81,84,89,95,104,107,123,126,151,157],"dynamic":[35],"behaviour":[36],"that":[38],"scheme.":[39,86,97],"earlier":[42,143],"study,":[43],"Sharma":[44],"and":[45,64],"Arora":[46],"(2015)":[47],"did":[48],"not":[49,120,146,163],"discuss":[50],"these":[51],"properties.":[52],"Furthermore,":[53],"was":[58],"shown":[59],"using":[60],"Taylor":[61],"series":[62],"expansions":[63],"hypotheses":[65,105],"up":[66,111],"fourth":[69],"derivative":[71],"or":[72],"even":[73],"higher":[74],"function":[77],"involved":[78],"which":[79],"restrict":[80],"applicability":[82,124],"proposed":[85,96,108,141],"However,":[87],"only":[88,121],"first":[90,113],"derivatives":[92],"appear":[93],"To":[98],"overcome":[99],"problem,":[101],"present":[103],"for":[106],"scheme":[109],"maximum":[110],"derivative.":[115],"way,":[118],"expand":[122],"methods":[127],"but":[128],"suggest":[130],"domain.":[132],"Finally,":[133],"variety":[135],"concrete":[137],"numerical":[138],"examples":[139],"are":[140],"where":[142],"studies":[144],"can":[145],"be":[147],"applied":[148],"obtain":[150],"solutions":[152],"equations":[155],"on":[156],"other":[158],"hand":[159],"our":[160],"does":[162],"exhibit":[164],"type":[166],"problem/restriction.":[168]},"counts_by_year":[{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}