{"id":"https://openalex.org/W4294958832","doi":"https://doi.org/10.3390/sym14091829","title":"Some New Quantum Numerical Techniques for Solving Nonlinear Equations","display_name":"Some New Quantum Numerical Techniques for Solving Nonlinear Equations","publication_year":2022,"publication_date":"2022-09-03","ids":{"openalex":"https://openalex.org/W4294958832","doi":"https://doi.org/10.3390/sym14091829"},"language":"en","primary_location":{"id":"doi:10.3390/sym14091829","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14091829","pdf_url":"https://www.mdpi.com/2073-8994/14/9/1829/pdf?version=1662363411","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/2073-8994/14/9/1829/pdf?version=1662363411","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089496116","display_name":"Kamsing Nonlaopon","orcid":"https://orcid.org/0000-0002-7469-5402"},"institutions":[{"id":"https://openalex.org/I179193067","display_name":"Khon Kaen University","ror":"https://ror.org/03cq4gr50","country_code":"TH","type":"education","lineage":["https://openalex.org/I179193067"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Kamsing Nonlaopon","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand"],"raw_orcid":"https://orcid.org/0000-0002-7469-5402","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand","institution_ids":["https://openalex.org/I179193067"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072105958","display_name":"Awais Gul Khan","orcid":"https://orcid.org/0000-0003-4914-5959"},"institutions":[{"id":"https://openalex.org/I194348271","display_name":"Government College University, Faisalabad","ror":"https://ror.org/051zgra59","country_code":"PK","type":"education","lineage":["https://openalex.org/I194348271"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Awais Gul Khan","raw_affiliation_strings":["Department of Mathematics, Government College University, Faisalabad 54000, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Government College University, Faisalabad 54000, Pakistan","institution_ids":["https://openalex.org/I194348271"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069604669","display_name":"Farah Ameen","orcid":null},"institutions":[{"id":"https://openalex.org/I194348271","display_name":"Government College University, Faisalabad","ror":"https://ror.org/051zgra59","country_code":"PK","type":"education","lineage":["https://openalex.org/I194348271"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Farah Ameen","raw_affiliation_strings":["Department of Mathematics, Government College University, Faisalabad 54000, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Government College University, Faisalabad 54000, Pakistan","institution_ids":["https://openalex.org/I194348271"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035904409","display_name":"Muhammad Uzair Awan","orcid":"https://orcid.org/0000-0002-1019-9485"},"institutions":[{"id":"https://openalex.org/I194348271","display_name":"Government College University, Faisalabad","ror":"https://ror.org/051zgra59","country_code":"PK","type":"education","lineage":["https://openalex.org/I194348271"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Muhammad Uzair Awan","raw_affiliation_strings":["Department of Mathematics, Government College University, Faisalabad 54000, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-1019-9485","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Government College University, Faisalabad 54000, Pakistan","institution_ids":["https://openalex.org/I194348271"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009771078","display_name":"Clemente Cesarano","orcid":null},"institutions":[{"id":"https://openalex.org/I4210155399","display_name":"UniNettuno University","ror":"https://ror.org/04q0nep37","country_code":"IT","type":"education","lineage":["https://openalex.org/I4210155399"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Clemente Cesarano","raw_affiliation_strings":["Section of Mathematics, International Telematic University Uninettuno, CorsoVittorio Emanuele II, 39, 00186 Roma, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Section of Mathematics, International Telematic University Uninettuno, CorsoVittorio Emanuele II, 39, 00186 Roma, Italy","institution_ids":["https://openalex.org/I4210155399"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5035904409"],"corresponding_institution_ids":["https://openalex.org/I194348271"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.2809,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.761205,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"14","issue":"9","first_page":"1829","last_page":"1829"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9898999929428101,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9722999930381775,"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/nonlinear-system","display_name":"Nonlinear system","score":0.6969746351242065},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6736262440681458},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.5704635977745056},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5679770708084106},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5432194471359253},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5309801697731018},{"id":"https://openalex.org/keywords/midpoint","display_name":"Midpoint","score":0.5050056576728821},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.45406267046928406},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43933433294296265},{"id":"https://openalex.org/keywords/local-convergence","display_name":"Local convergence","score":0.43911707401275635},{"id":"https://openalex.org/keywords/midpoint-method","display_name":"Midpoint method","score":0.4225490689277649},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.31431812047958374},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20927110314369202},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0984812080860138},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08243808150291443},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06888765096664429}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6969746351242065},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6736262440681458},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5704635977745056},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5679770708084106},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5432194471359253},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5309801697731018},{"id":"https://openalex.org/C34130140","wikidata":"https://www.wikidata.org/wiki/Q1645406","display_name":"Midpoint","level":2,"score":0.5050056576728821},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.45406267046928406},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43933433294296265},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.43911707401275635},{"id":"https://openalex.org/C85807060","wikidata":"https://www.wikidata.org/wiki/Q17103851","display_name":"Midpoint method","level":2,"score":0.4225490689277649},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.31431812047958374},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20927110314369202},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0984812080860138},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08243808150291443},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06888765096664429},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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":3,"locations":[{"id":"doi:10.3390/sym14091829","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14091829","pdf_url":"https://www.mdpi.com/2073-8994/14/9/1829/pdf?version=1662363411","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:92e131d852ff4160a730fef1b34c45bf","is_oa":true,"landing_page_url":"https://doaj.org/article/92e131d852ff4160a730fef1b34c45bf","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":"Symmetry, Vol 14, Iss 9, p 1829 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/9/1829/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14091829","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 14; Issue 9; Pages: 1829","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14091829","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14091829","pdf_url":"https://www.mdpi.com/2073-8994/14/9/1829/pdf?version=1662363411","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":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4294958832.pdf"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W781630492","https://openalex.org/W1969004631","https://openalex.org/W1992709107","https://openalex.org/W1995881804","https://openalex.org/W2025487819","https://openalex.org/W2039503680","https://openalex.org/W2047330144","https://openalex.org/W2109195981","https://openalex.org/W2326379377","https://openalex.org/W2484595386","https://openalex.org/W2795230022","https://openalex.org/W2954394215","https://openalex.org/W2963848485","https://openalex.org/W2998968103","https://openalex.org/W3041464168","https://openalex.org/W3091499157","https://openalex.org/W3110287239","https://openalex.org/W3133938021","https://openalex.org/W3161329759","https://openalex.org/W3162085095","https://openalex.org/W4240426777","https://openalex.org/W6622728594","https://openalex.org/W6649279609","https://openalex.org/W6656439921","https://openalex.org/W6676835866","https://openalex.org/W6786414066","https://openalex.org/W6790765905"],"related_works":["https://openalex.org/W2391598905","https://openalex.org/W2330791370","https://openalex.org/W2072226187","https://openalex.org/W37565017","https://openalex.org/W2357395917","https://openalex.org/W3091779247","https://openalex.org/W2391440809","https://openalex.org/W3018722875","https://openalex.org/W4388044523","https://openalex.org/W2357624778"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"introduce":[4],"some":[5],"new":[6,38],"quantum":[7],"numerical":[8],"techniques":[9],"of":[10,26,28],"midpoint":[11],"and":[12],"trapezoidal":[13],"type":[14],"essentially":[15],"by":[16],"using":[17],"the":[18,24,37,45],"decomposition":[19],"technique.":[20],"We":[21],"also":[22],"check":[23],"order":[25],"convergence":[27],"our":[29],"suggested":[30],"iterative":[31],"methods.":[32],"Numerical":[33],"examples":[34],"demonstrate":[35],"that":[36],"q-iterative":[39],"methods":[40],"can":[41],"generate":[42],"solutions":[43],"to":[44],"nonlinear":[46],"equations":[47],"with":[48],"acceptable":[49],"accuracy.":[50]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}