{"id":"https://openalex.org/W4323314963","doi":"https://doi.org/10.3390/axioms12030270","title":"Approximating Multiple Roots of Applied Mathematical Problems Using Iterative Techniques","display_name":"Approximating Multiple Roots of Applied Mathematical Problems Using Iterative Techniques","publication_year":2023,"publication_date":"2023-03-06","ids":{"openalex":"https://openalex.org/W4323314963","doi":"https://doi.org/10.3390/axioms12030270"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12030270","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/axioms12030270","pdf_url":"https://www.mdpi.com/2075-1680/12/3/270/pdf","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://www.mdpi.com/2075-1680/12/3/270/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078192871","display_name":"Ramandeep Behl","orcid":"https://orcid.org/0000-0003-1505-8945"},"institutions":[{"id":"https://openalex.org/I185163786","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74","country_code":"SA","type":"education","lineage":["https://openalex.org/I185163786"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Ramandeep Behl","raw_affiliation_strings":["Mathematical Modelling and Applied Computation Research Group (MMAC), Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-1505-8945","affiliations":[{"raw_affiliation_string":"Mathematical Modelling and Applied Computation Research Group (MMAC), Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033526761","display_name":"Himani Arora","orcid":null},"institutions":[{"id":"https://openalex.org/I165682329","display_name":"Guru Nanak Dev University","ror":"https://ror.org/05ghzpa93","country_code":"IN","type":"education","lineage":["https://openalex.org/I165682329"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Himani Arora","raw_affiliation_strings":["Department of Mathematics, Guru Nanak Dev University, Amritsar 143005, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Guru Nanak Dev University, Amritsar 143005, India","institution_ids":["https://openalex.org/I165682329"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024974938","display_name":"Eulalia Mart\u0131\u0301nez","orcid":"https://orcid.org/0000-0003-2869-4334"},"institutions":[{"id":"https://openalex.org/I60053951","display_name":"Universitat Polit\u00e8cnica de Val\u00e8ncia","ror":"https://ror.org/01460j859","country_code":"ES","type":"education","lineage":["https://openalex.org/I60053951"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Eulalia Mart\u00ednez","raw_affiliation_strings":["Instituto Universitario de Matem\u00e1tica Multidisciplinar, Universitat Polit\u00e8cnica de Val\u00e8ncia, 46022 Val\u00e8ncia, Spain"],"raw_orcid":"https://orcid.org/0000-0003-2869-4334","affiliations":[{"raw_affiliation_string":"Instituto Universitario de Matem\u00e1tica Multidisciplinar, Universitat Polit\u00e8cnica de Val\u00e8ncia, 46022 Val\u00e8ncia, Spain","institution_ids":["https://openalex.org/I60053951"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083285892","display_name":"Tajinder Singh","orcid":null},"institutions":[{"id":"https://openalex.org/I165682329","display_name":"Guru Nanak Dev University","ror":"https://ror.org/05ghzpa93","country_code":"IN","type":"education","lineage":["https://openalex.org/I165682329"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Tajinder Singh","raw_affiliation_strings":["Department of Mathematics, Guru Nanak Dev University, Amritsar 143005, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Guru Nanak Dev University, Amritsar 143005, India","institution_ids":["https://openalex.org/I165682329"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5024974938"],"corresponding_institution_ids":["https://openalex.org/I60053951"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.3807,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.48237941,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"12","issue":"3","first_page":"270","last_page":"270"},"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":0.9904999732971191,"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":0.983299970626831,"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/mathematics","display_name":"Mathematics","score":0.6779722571372986},{"id":"https://openalex.org/keywords/multiplicity","display_name":"Multiplicity (mathematics)","score":0.6381779909133911},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.6306671500205994},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.6105462312698364},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6061795353889465},{"id":"https://openalex.org/keywords/local-convergence","display_name":"Local convergence","score":0.5614998936653137},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5587460398674011},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.5379157066345215},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5139896273612976},{"id":"https://openalex.org/keywords/fr\u00e9chet-derivative","display_name":"Fr\u00e9chet derivative","score":0.49616488814353943},{"id":"https://openalex.org/keywords/approximation-error","display_name":"Approximation error","score":0.4914025068283081},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3238520920276642},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3020005524158478},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19910627603530884},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11974695324897766}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6779722571372986},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.6381779909133911},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.6306671500205994},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.6105462312698364},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6061795353889465},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.5614998936653137},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5587460398674011},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.5379157066345215},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5139896273612976},{"id":"https://openalex.org/C118335899","wikidata":"https://www.wikidata.org/wiki/Q1305350","display_name":"Fr\u00e9chet derivative","level":3,"score":0.49616488814353943},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.4914025068283081},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3238520920276642},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3020005524158478},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19910627603530884},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11974695324897766},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"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/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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/axioms12030270","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/axioms12030270","pdf_url":"https://www.mdpi.com/2075-1680/12/3/270/pdf","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:riunet.upv.es:10251/202998","is_oa":true,"landing_page_url":"http://hdl.handle.net/10251/202998","pdf_url":null,"source":{"id":"https://openalex.org/S4306401500","display_name":"RiuNet (Politechnical University of Valencia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I60053951","host_organization_name":"Universitat Polit\u00e8cnica de Val\u00e8ncia","host_organization_lineage":["https://openalex.org/I60053951"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:1f2b6d15de85429e88435f1f5218e542","is_oa":true,"landing_page_url":"https://doaj.org/article/1f2b6d15de85429e88435f1f5218e542","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 12, Iss 3, p 270 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/12/3/270/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms12030270","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":"Axioms; Volume 12; Issue 3; Pages: 270","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms12030270","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/axioms12030270","pdf_url":"https://www.mdpi.com/2075-1680/12/3/270/pdf","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":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4323314963.pdf","grobid_xml":"https://content.openalex.org/works/W4323314963.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W169252370","https://openalex.org/W1495800631","https://openalex.org/W1989809391","https://openalex.org/W2004914005","https://openalex.org/W2017299431","https://openalex.org/W2032105013","https://openalex.org/W2039381603","https://openalex.org/W2047067568","https://openalex.org/W2047164535","https://openalex.org/W2078749110","https://openalex.org/W2090247181","https://openalex.org/W2895267754","https://openalex.org/W2936727600","https://openalex.org/W2990474610","https://openalex.org/W3021906145","https://openalex.org/W3036761082","https://openalex.org/W3038757318","https://openalex.org/W3093067222","https://openalex.org/W3134686303"],"related_works":["https://openalex.org/W2245126542","https://openalex.org/W2154833956","https://openalex.org/W2097846334","https://openalex.org/W2547159309","https://openalex.org/W2609905241","https://openalex.org/W4247076037","https://openalex.org/W2531699496","https://openalex.org/W2314912066","https://openalex.org/W2165024463","https://openalex.org/W4236948532"],"abstract_inverted_index":{"In":[0],"this":[1,44],"study,":[2],"we":[3,41,67],"suggest":[4],"a":[5,23],"new":[6,64],"iterative":[7,10,46,60,65],"family":[8],"of":[9,28,54,72,98,135,140,144],"methods":[11,47],"for":[12,95,113],"approximating":[13],"the":[14,26,32,35,52,55,96,108,114,124,130],"roots":[15,30],"with":[16],"multiplicity":[17,117],"in":[18,25,31,43,58,107,133],"nonlinear":[19,36],"equations.":[20],"We":[21],"found":[22],"lack":[24],"approximation":[27],"multiple":[29],"case":[33,115],"that":[34,48],"operator":[37,57],"be":[38],"non-differentiable.":[39],"So,":[40],"present,":[42],"paper,":[45],"do":[49],"not":[50],"use":[51],"derivative":[53],"non-linear":[56],"their":[59],"expression.":[61],"With":[62],"our":[63,99],"technique,":[66],"find":[68],"better":[69],"numerical":[70,121],"results":[71,122],"Planck\u2019s":[73],"radiation,":[74],"Van":[75],"Der":[76],"Waals,":[77],"Beam":[78],"designing,":[79],"and":[80,89,111,147],"Isothermal":[81],"continuous":[82],"stirred":[83],"tank":[84],"reactor":[85],"problems.":[86],"Divided":[87],"difference":[88,150],"weight":[90],"function":[91],"approaches":[92],"are":[93],"adopted":[94],"construction":[97],"schemes.":[100],"The":[101,119],"convergence":[102,145],"order":[103,143],"is":[104],"studied":[105],"thoroughly":[106],"Theorems":[109],"1":[110],"2,":[112],"when":[116],"p\u22652.":[118],"obtained":[120],"illustrate":[123],"preferable":[125],"outcomes":[126],"as":[127],"compared":[128],"to":[129],"existing":[131],"ones":[132],"terms":[134],"absolute":[136,148],"residual":[137],"errors,":[138],"number":[139],"iterations,":[141],"computational":[142],"(COC),":[146],"error":[149],"between":[151],"two":[152],"consecutive":[153],"iterations.":[154]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-06-15T08:34:33.830935","created_date":"2023-03-07T00:00:00"}
