{"id":"https://openalex.org/W2926888556","doi":"https://doi.org/10.1109/access.2019.2906470","title":"Higher Order Numerical Approaches for Nonlinear Equations by Decomposition Technique","display_name":"Higher Order Numerical Approaches for Nonlinear Equations by Decomposition Technique","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2926888556","doi":"https://doi.org/10.1109/access.2019.2906470","mag":"2926888556"},"language":"en","primary_location":{"id":"doi:10.1109/access.2019.2906470","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2906470","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08681066.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08681066.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057557499","display_name":"Abdulghani Alharbi","orcid":"https://orcid.org/0000-0002-1430-4684"},"institutions":[{"id":"https://openalex.org/I23075662","display_name":"Taibah University","ror":"https://ror.org/01xv1nn60","country_code":"SA","type":"education","lineage":["https://openalex.org/I23075662"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Abdulghani Ragaa Alharbi","raw_affiliation_strings":["Department of Mathematics, Taibah University, Medina, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Taibah University, Medina, Saudi Arabia","institution_ids":["https://openalex.org/I23075662"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080436268","display_name":"Muhammad Imran Faisal","orcid":"https://orcid.org/0000-0002-4169-4366"},"institutions":[{"id":"https://openalex.org/I23075662","display_name":"Taibah University","ror":"https://ror.org/01xv1nn60","country_code":"SA","type":"education","lineage":["https://openalex.org/I23075662"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Muhammed Imran Faisal","raw_affiliation_strings":["Department of Mathematics, Taibah University, Medina, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Taibah University, Medina, Saudi Arabia","institution_ids":["https://openalex.org/I23075662"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079993624","display_name":"Farooq Ahmed Shah","orcid":"https://orcid.org/0000-0001-7419-423X"},"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":false,"raw_author_name":"Farooq Ahmed Shah","raw_affiliation_strings":["Department of Mathematics, COMSATS University Islamabad, Attock, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, COMSATS University Islamabad, Attock, Pakistan","institution_ids":["https://openalex.org/I16076960"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077022343","display_name":"Muhammad Waseem","orcid":"https://orcid.org/0000-0001-5903-0122"},"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":false,"raw_author_name":"Muhammad Waseem","raw_affiliation_strings":["Department of Mathematics, COMSATS University Islamabad, Vehari, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, COMSATS University Islamabad, Vehari, Pakistan","institution_ids":["https://openalex.org/I16076960"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5114041846","display_name":"Roman Ullah","orcid":null},"institutions":[{"id":"https://openalex.org/I4210114766","display_name":"Muscat College","ror":"https://ror.org/01zhpv322","country_code":"OM","type":"education","lineage":["https://openalex.org/I4210114766"]}],"countries":["OM"],"is_corresponding":false,"raw_author_name":"Roman Ullah","raw_affiliation_strings":["Department of Mathematics, Muscat College, Muscat, Oman"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Muscat College, Muscat, Oman","institution_ids":["https://openalex.org/I4210114766"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067518655","display_name":"Saira Sherbaz","orcid":null},"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":false,"raw_author_name":"Saira Sherbaz","raw_affiliation_strings":["Department of Mathematics, COMSATS University Islamabad, Attock, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, COMSATS University Islamabad, Attock, Pakistan","institution_ids":["https://openalex.org/I16076960"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5057557499"],"corresponding_institution_ids":["https://openalex.org/I23075662"],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":3.5424,"has_fulltext":true,"cited_by_count":20,"citation_normalized_percentile":{"value":0.92776848,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"7","issue":null,"first_page":"44329","last_page":"44337"},"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":0.9869999885559082,"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":0.977400004863739,"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/nonlinear-system","display_name":"Nonlinear system","score":0.7826541662216187},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.6120209693908691},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.5761318802833557},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5463209748268127},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5445918440818787},{"id":"https://openalex.org/keywords/decomposition-method","display_name":"Decomposition method (queueing theory)","score":0.5166323781013489},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.45834797620773315},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.44874945282936096},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4071119427680969},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40703830122947693},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2927115857601166}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7826541662216187},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.6120209693908691},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.5761318802833557},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5463209748268127},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5445918440818787},{"id":"https://openalex.org/C2778258933","wikidata":"https://www.wikidata.org/wiki/Q16918986","display_name":"Decomposition method (queueing theory)","level":2,"score":0.5166323781013489},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.45834797620773315},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.44874945282936096},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4071119427680969},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40703830122947693},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2927115857601166},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","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},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2019.2906470","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2906470","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08681066.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:811169f63aac4e268390027483c4b8e6","is_oa":true,"landing_page_url":"https://doaj.org/article/811169f63aac4e268390027483c4b8e6","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":"IEEE Access, Vol 7, Pp 44329-44337 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2019.2906470","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2906470","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08681066.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5692923670","display_name":null,"funder_award_id":"5418/Federal/NRPU/ R&D/HEC/2016","funder_id":"https://openalex.org/F4320322799","funder_display_name":"Higher Education Commission, Pakistan"}],"funders":[{"id":"https://openalex.org/F4320311330","display_name":"COMSATS Institute of Information Technology","ror":"https://ror.org/00nqqvk19"},{"id":"https://openalex.org/F4320322799","display_name":"Higher Education Commission, Pakistan","ror":"https://ror.org/038y3sz68"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2926888556.pdf","grobid_xml":"https://content.openalex.org/works/W2926888556.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W1550563201","https://openalex.org/W1969004631","https://openalex.org/W1970196459","https://openalex.org/W1984547000","https://openalex.org/W1985698733","https://openalex.org/W1992709107","https://openalex.org/W1994625348","https://openalex.org/W1995881804","https://openalex.org/W2042109765","https://openalex.org/W2048632019","https://openalex.org/W2049247717","https://openalex.org/W2050741433","https://openalex.org/W2059101080","https://openalex.org/W2069144579","https://openalex.org/W2089470918","https://openalex.org/W2109195981","https://openalex.org/W2131826789","https://openalex.org/W2144399742","https://openalex.org/W2186013578","https://openalex.org/W2296409083","https://openalex.org/W2760618399","https://openalex.org/W2790606970","https://openalex.org/W2797215386","https://openalex.org/W4240426777","https://openalex.org/W6648691755","https://openalex.org/W6662941123","https://openalex.org/W6686474223"],"related_works":["https://openalex.org/W2358591430","https://openalex.org/W2330487432","https://openalex.org/W2153629319","https://openalex.org/W2350788688","https://openalex.org/W2104316494","https://openalex.org/W239705756","https://openalex.org/W156119379","https://openalex.org/W2082139080","https://openalex.org/W2357287617","https://openalex.org/W4231015910"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"a":[3,76,85],"unique":[4],"decomposition":[5],"technique":[6],"is":[7],"implemented":[8],"along":[9],"with":[10],"an":[11],"auxiliary":[12],"function":[13],"for":[14,27,90],"the":[15,38,49,63,92],"best":[16],"implementation.":[17],"Some":[18,43],"new":[19,72],"and":[20,25,54,57,82,87],"efficient":[21],"techniques":[22,31],"are":[23,32,62,75,83],"introduced":[24],"analyzed":[26],"nonlinear":[28,41,95],"equations.":[29,42,96],"These":[30,71],"higher":[33],"ordered":[34],"in":[35,79],"approaching":[36],"to":[37],"root":[39],"of":[40,66,94],"existing":[44,80],"classical":[45],"methods":[46,81],"such":[47],"as":[48],"Newton":[50],"method,":[51,53],"Halley":[52],"Traub's":[55],"approach":[56],"their":[58],"various":[59],"modified":[60],"forms":[61],"special":[64],"cases":[65],"these":[67],"newly":[68],"purposed":[69],"schemes.":[70],"iterative":[73],"schemes":[74],"good":[77],"addition":[78],"also":[84],"comprehensive":[86],"generalized":[88],"form":[89],"finding":[91],"solution":[93]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":6},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
