{"id":"https://openalex.org/W4406669709","doi":"https://doi.org/10.3390/axioms14020077","title":"On the Derivation of a Fast Solver for Nonlinear Systems of Equations Utilizing Frozen Substeps with Applications","display_name":"On the Derivation of a Fast Solver for Nonlinear Systems of Equations Utilizing Frozen Substeps with Applications","publication_year":2025,"publication_date":"2025-01-21","ids":{"openalex":"https://openalex.org/W4406669709","doi":"https://doi.org/10.3390/axioms14020077"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14020077","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14020077","pdf_url":"https://www.mdpi.com/2075-1680/14/2/77/pdf?version=1737464791","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/2075-1680/14/2/77/pdf?version=1737464791","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100448079","display_name":"Mingming Liu","orcid":"https://orcid.org/0000-0002-8988-2104"},"institutions":[{"id":"https://openalex.org/I7726996","display_name":"Henan University of Economic and Law","ror":"https://ror.org/000jtc944","country_code":"CN","type":"education","lineage":["https://openalex.org/I7726996"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Mingming Liu","raw_affiliation_strings":["School of Statistics and Big Data, Zhengzhou College of Finance and Economics, Zhengzhou 450000, China"],"affiliations":[{"raw_affiliation_string":"School of Statistics and Big Data, Zhengzhou College of Finance and Economics, Zhengzhou 450000, China","institution_ids":["https://openalex.org/I7726996"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057765710","display_name":"Stanford Shateyi","orcid":"https://orcid.org/0000-0002-5829-8634"},"institutions":[{"id":"https://openalex.org/I84929415","display_name":"University of Venda","ror":"https://ror.org/0338xea48","country_code":"ZA","type":"education","lineage":["https://openalex.org/I84929415"]}],"countries":["ZA"],"is_corresponding":true,"raw_author_name":"Stanford Shateyi","raw_affiliation_strings":["Department of Mathematics and Applied Mathematics, School of Mathematical and Natural Sciences, University of Venda, P. Bag X5050, Thohoyandou 0950, South Africa"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Applied Mathematics, School of Mathematical and Natural Sciences, University of Venda, P. Bag X5050, Thohoyandou 0950, South Africa","institution_ids":["https://openalex.org/I84929415"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5057765710"],"corresponding_institution_ids":["https://openalex.org/I84929415"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02279702,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"2","first_page":"77","last_page":"77"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9979000091552734,"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"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9937999844551086,"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/nonlinear-system","display_name":"Nonlinear system","score":0.5863602161407471},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.5826404094696045},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4229484498500824},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3936028480529785},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38523462414741516},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3304526209831238},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2563663125038147},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.20316258072853088},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.0985143780708313},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07830733060836792}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5863602161407471},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.5826404094696045},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4229484498500824},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3936028480529785},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38523462414741516},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3304526209831238},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2563663125038147},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.20316258072853088},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0985143780708313},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07830733060836792},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14020077","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14020077","pdf_url":"https://www.mdpi.com/2075-1680/14/2/77/pdf?version=1737464791","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:doaj.org/article:e4ce1d98d25846b3a19c01572532588a","is_oa":true,"landing_page_url":"https://doaj.org/article/e4ce1d98d25846b3a19c01572532588a","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 14, Iss 2, p 77 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14020077","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14020077","pdf_url":"https://www.mdpi.com/2075-1680/14/2/77/pdf?version=1737464791","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4406669709.pdf","grobid_xml":"https://content.openalex.org/works/W4406669709.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W41675498","https://openalex.org/W2011023522","https://openalex.org/W2022703159","https://openalex.org/W2027823200","https://openalex.org/W2040119000","https://openalex.org/W2152208093","https://openalex.org/W2260711816","https://openalex.org/W2305389348","https://openalex.org/W2502051282","https://openalex.org/W2542167254","https://openalex.org/W2971375020","https://openalex.org/W4224231919","https://openalex.org/W4225616427","https://openalex.org/W4229078726","https://openalex.org/W4298003856","https://openalex.org/W4323975531","https://openalex.org/W4390099212","https://openalex.org/W4400134983","https://openalex.org/W6754506741"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"In":[0],"this":[1],"manuscript,":[2],"we":[3],"propose":[4],"a":[5,31],"multi-step":[6],"framework":[7],"for":[8,55],"solving":[9],"nonlinear":[10,78],"systems":[11],"of":[12,72],"algebraic":[13],"equations.":[14],"To":[15],"improve":[16],"the":[17,20,27,37,70,73],"solver\u2019s":[18],"efficiency,":[19],"Jacobian":[21,47],"matrix":[22],"is":[23,34],"held":[24],"constant":[25],"during":[26],"second":[28],"sub-step,":[29],"while":[30],"specialized":[32],"strategy":[33],"applied":[35],"in":[36,76],"third":[38],"sub-step":[39],"to":[40,68],"maximize":[41],"convergence":[42,54,61],"speed":[43],"without":[44],"necessitating":[45],"additional":[46],"evaluations.":[48],"The":[49],"proposed":[50,74],"method":[51],"achieves":[52],"fifth-order":[53],"simple":[56],"roots,":[57],"with":[58],"its":[59],"theoretical":[60],"established.":[62],"Finally,":[63],"computational":[64],"experiments":[65],"are":[66],"conducted":[67],"illustrate":[69],"performance":[71],"solver":[75],"addressing":[77],"equation":[79],"systems.":[80]},"counts_by_year":[],"updated_date":"2026-03-08T06:56:09.383167","created_date":"2025-10-10T00:00:00"}
