{"id":"https://openalex.org/W4315853562","doi":"https://doi.org/10.3390/sym15010228","title":"A Family of Higher Order Scheme for Multiple Roots","display_name":"A Family of Higher Order Scheme for Multiple Roots","publication_year":2023,"publication_date":"2023-01-13","ids":{"openalex":"https://openalex.org/W4315853562","doi":"https://doi.org/10.3390/sym15010228"},"language":"en","primary_location":{"id":"doi:10.3390/sym15010228","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15010228","pdf_url":"https://www.mdpi.com/2073-8994/15/1/228/pdf?version=1673597657","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/15/1/228/pdf?version=1673597657","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","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, Punjab, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Guru Nanak Dev University, Amritsar 143005, Punjab, India","institution_ids":["https://openalex.org/I165682329"]}]},{"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":true,"raw_author_name":"Himani Arora","raw_affiliation_strings":["Department of Mathematics, Guru Nanak Dev University, Amritsar 143005, Punjab, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Guru Nanak Dev University, Amritsar 143005, Punjab, India","institution_ids":["https://openalex.org/I165682329"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006002266","display_name":"Lorentz J\u00e4ntschi","orcid":"https://orcid.org/0000-0001-8524-743X"},"institutions":[{"id":"https://openalex.org/I158333966","display_name":"Technical University of Cluj-Napoca","ror":"https://ror.org/03r8nwp71","country_code":"RO","type":"education","lineage":["https://openalex.org/I158333966"]},{"id":"https://openalex.org/I3125347698","display_name":"Babe\u0219-Bolyai University","ror":"https://ror.org/02rmd1t30","country_code":"RO","type":"education","lineage":["https://openalex.org/I3125347698"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"Lorentz J\u00e4ntschi","raw_affiliation_strings":["Department of Physics and Chemistry, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania","Institute of Doctoral Studies, Babe\u015f-Bolyai University, 400084 Cluj-Napoca, Romania"],"raw_orcid":"https://orcid.org/0000-0001-8524-743X","affiliations":[{"raw_affiliation_string":"Department of Physics and Chemistry, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania","institution_ids":["https://openalex.org/I158333966"]},{"raw_affiliation_string":"Institute of Doctoral Studies, Babe\u015f-Bolyai University, 400084 Cluj-Napoca, Romania","institution_ids":["https://openalex.org/I3125347698"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5006002266","https://openalex.org/A5033526761"],"corresponding_institution_ids":["https://openalex.org/I158333966","https://openalex.org/I165682329","https://openalex.org/I3125347698"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.9427,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.81681682,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"15","issue":"1","first_page":"228","last_page":"228"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9868000149726868,"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"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.963100016117096,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.6380394697189331},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6320468187332153},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5930737853050232},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.5711077451705933},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.532965898513794},{"id":"https://openalex.org/keywords/attraction","display_name":"Attraction","score":0.5287801027297974},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5209378004074097},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.4855458438396454},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36095112562179565},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3567832112312317},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24854683876037598},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.23841753602027893}],"concepts":[{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.6380394697189331},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6320468187332153},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5930737853050232},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.5711077451705933},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.532965898513794},{"id":"https://openalex.org/C2778364177","wikidata":"https://www.wikidata.org/wiki/Q2247133","display_name":"Attraction","level":2,"score":0.5287801027297974},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5209378004074097},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4855458438396454},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36095112562179565},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3567832112312317},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24854683876037598},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.23841753602027893},{"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym15010228","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15010228","pdf_url":"https://www.mdpi.com/2073-8994/15/1/228/pdf?version=1673597657","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:cfaedee9e6b747b5ae55c261f3bac5ae","is_oa":false,"landing_page_url":"https://doaj.org/article/cfaedee9e6b747b5ae55c261f3bac5ae","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 15, Iss 1, p 228 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/1/228/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15010228","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":"Symmetry; Volume 15; Issue 1; Pages: 228","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym15010228","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15010228","pdf_url":"https://www.mdpi.com/2073-8994/15/1/228/pdf?version=1673597657","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320721","display_name":"Council of Scientific and Industrial Research, India","ror":"https://ror.org/021wm7p51"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4315853562.pdf"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W169252370","https://openalex.org/W1989019717","https://openalex.org/W2004914005","https://openalex.org/W2008808290","https://openalex.org/W2013195662","https://openalex.org/W2017299431","https://openalex.org/W2038044774","https://openalex.org/W2039381603","https://openalex.org/W2047067568","https://openalex.org/W2048270647","https://openalex.org/W2086563658","https://openalex.org/W2109195981","https://openalex.org/W2115099530","https://openalex.org/W2130261568","https://openalex.org/W2213022072","https://openalex.org/W2220300957","https://openalex.org/W2293874761","https://openalex.org/W2310743009","https://openalex.org/W2628846632","https://openalex.org/W2937669490","https://openalex.org/W2955467866","https://openalex.org/W2956523656","https://openalex.org/W2962856795","https://openalex.org/W2967626987","https://openalex.org/W2990474610","https://openalex.org/W3017811005","https://openalex.org/W3026531385","https://openalex.org/W3037894255","https://openalex.org/W3038757318","https://openalex.org/W3112073755","https://openalex.org/W3134686303","https://openalex.org/W3185041061","https://openalex.org/W4213078570","https://openalex.org/W4224231919","https://openalex.org/W4292604635","https://openalex.org/W4294958998","https://openalex.org/W4295943419","https://openalex.org/W4298003856"],"related_works":["https://openalex.org/W4386786398","https://openalex.org/W2138293586","https://openalex.org/W4282832460","https://openalex.org/W4319783074","https://openalex.org/W4255464147","https://openalex.org/W2080052720","https://openalex.org/W1503179180","https://openalex.org/W4319778501","https://openalex.org/W2171384148","https://openalex.org/W2021797003"],"abstract_inverted_index":{"We":[0],"have":[1,139],"developed":[2],"a":[3,45,52,59,61,67],"two-point":[4],"iterative":[5],"scheme":[6],"for":[7],"multiple":[8],"roots":[9],"that":[10,141],"achieves":[11],"fifth":[12,134],"order":[13],"convergence":[14],"by":[15],"using":[16],"two":[17,21],"function":[18,27,37,46,53],"evaluations":[19,23],"and":[20,49,64,80,103,123],"derivative":[22],"each":[24],"iteration.":[25],"Weight":[26],"approach":[28],"is":[29,41,44,51,60,66,77],"utilized":[30],"to":[31,91,118,124],"frame":[32],"the":[33,73,82,93,120,126,142,148,152],"scheme.":[34],"The":[35,70,136],"weight":[36],"named":[38],"as":[39],"R(\u03c5t)":[40],"used,":[42],"which":[43],"of":[47,54,72,84,101,107,133,151],"\u03c5t,":[48],"\u03c5t":[50],"\u03c9t,":[55],"i.e.,":[56],"\u03c5t=\u03c9t1+a\u03c9t,":[57],"where":[58],"real":[62],"number":[63],"\u03c9t=g(yt)g(xt)1m\u02dc":[65],"multi-valued":[68],"function.":[69],"consistency":[71],"newly":[74],"generated":[75],"methods":[76,95],"ensured":[78],"numerically":[79],"through":[81],"basins":[83,100,106],"attraction.":[85],"Four":[86],"complex":[87],"functions":[88],"are":[89,116,145],"considered":[90],"compare":[92],"new":[94,143],"with":[96,129],"existing":[97,149],"schemes":[98,128,132,144,150],"via":[99],"attraction,":[102],"all":[104],"provided":[105],"attraction":[108],"possess":[109],"reflection":[110],"symmetry.":[111],"Further,":[112],"five":[113],"numerical":[114],"examples":[115],"used":[117],"verify":[119],"theoretical":[121],"results":[122,137],"contrast":[125],"presented":[127],"some":[130],"recognized":[131],"order.":[135],"obtained":[138],"proved":[140],"better":[146],"than":[147],"same":[153],"nature.":[154]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
