{"id":"https://openalex.org/W7118065495","doi":"https://doi.org/10.1007/s12190-025-02739-y","title":"On the stability of a finite difference scheme for the nonlinear silicon problem","display_name":"On the stability of a finite difference scheme for the nonlinear silicon problem","publication_year":2026,"publication_date":"2026-01-03","ids":{"openalex":"https://openalex.org/W7118065495","doi":"https://doi.org/10.1007/s12190-025-02739-y"},"language":"en","primary_location":{"id":"doi:10.1007/s12190-025-02739-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s12190-025-02739-y","pdf_url":null,"source":{"id":"https://openalex.org/S199913245","display_name":"Journal of Applied Mathematics and Computing","issn_l":"1226-0061","issn":["1226-0061","1229-9499","1229-9502","1598-5865","1865-2085"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052845552","display_name":"Adriano Rodrigues de Melo","orcid":"https://orcid.org/0000-0002-3043-8906"},"institutions":[{"id":"https://openalex.org/I4210118451","display_name":"Instituto Federal Catarinense","ror":"https://ror.org/02f8h1m78","country_code":"BR","type":"facility","lineage":["https://openalex.org/I4210118451"]},{"id":"https://openalex.org/I52418104","display_name":"Universidade Federal do Paran\u00e1","ror":"https://ror.org/05syd6y78","country_code":"BR","type":"education","lineage":["https://openalex.org/I52418104"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Adriano Rodrigues de Melo","raw_affiliation_strings":["Catarinense Federal Institute, BR-280, Araquari, Santa Catarina, 89245-000, Brazil","Graduate Program in Numerical Methods in Engineering, Federal University of Paran\u00e1, Polytechnic Center, Curitiba, Paran\u00e1, 81530-000, Brazil"],"raw_orcid":"https://orcid.org/0000-0002-3043-8906","affiliations":[{"raw_affiliation_string":"Catarinense Federal Institute, BR-280, Araquari, Santa Catarina, 89245-000, Brazil","institution_ids":["https://openalex.org/I4210118451"]},{"raw_affiliation_string":"Graduate Program in Numerical Methods in Engineering, Federal University of Paran\u00e1, Polytechnic Center, Curitiba, Paran\u00e1, 81530-000, Brazil","institution_ids":["https://openalex.org/I52418104"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5121849870","display_name":"Marcio Augusto Villela Pinto","orcid":null},"institutions":[{"id":"https://openalex.org/I52418104","display_name":"Universidade Federal do Paran\u00e1","ror":"https://ror.org/05syd6y78","country_code":"BR","type":"education","lineage":["https://openalex.org/I52418104"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Marcio Augusto Villela Pinto","raw_affiliation_strings":["Department of Mechanical Engineering, Federal University of Paran\u00e1, Polytechnic Center, Curitiba, Paran\u00e1, 81530-000, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Federal University of Paran\u00e1, Polytechnic Center, Curitiba, Paran\u00e1, 81530-000, Brazil","institution_ids":["https://openalex.org/I52418104"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022834926","display_name":"Sebasti\u00e3o Romero Franco","orcid":"https://orcid.org/0000-0002-4580-5924"},"institutions":[{"id":"https://openalex.org/I3020652664","display_name":"Universidade Estadual do Paran\u00e1","ror":"https://ror.org/049rrx986","country_code":"BR","type":"education","lineage":["https://openalex.org/I3020652664"]},{"id":"https://openalex.org/I52418104","display_name":"Universidade Federal do Paran\u00e1","ror":"https://ror.org/05syd6y78","country_code":"BR","type":"education","lineage":["https://openalex.org/I52418104"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Sebasti\u00e3o Romero Franco","raw_affiliation_strings":["Department of Mathematics, State University of the Central West, Irati, Paran\u00e1, 84505-677, Brazil","Graduate Program in Numerical Methods in Engineering, Federal University of Paran\u00e1, Polytechnic Center, Curitiba, Paran\u00e1, 81530-000, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, State University of the Central West, Irati, Paran\u00e1, 84505-677, Brazil","institution_ids":["https://openalex.org/I3020652664"]},{"raw_affiliation_string":"Graduate Program in Numerical Methods in Engineering, Federal University of Paran\u00e1, Polytechnic Center, Curitiba, Paran\u00e1, 81530-000, Brazil","institution_ids":["https://openalex.org/I52418104"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5097632837","display_name":"Priscila Dombrovski Zen","orcid":"https://orcid.org/0000-0001-7826-4928"},"institutions":[{"id":"https://openalex.org/I52418104","display_name":"Universidade Federal do Paran\u00e1","ror":"https://ror.org/05syd6y78","country_code":"BR","type":"education","lineage":["https://openalex.org/I52418104"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Priscila Dombrovski Zen","raw_affiliation_strings":["Graduate Program in Numerical Methods in Engineering, Federal University of Paran\u00e1, Polytechnic Center, Curitiba, Paran\u00e1, 81530-000, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate Program in Numerical Methods in Engineering, Federal University of Paran\u00e1, Polytechnic Center, Curitiba, Paran\u00e1, 81530-000, Brazil","institution_ids":["https://openalex.org/I52418104"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5052845552"],"corresponding_institution_ids":["https://openalex.org/I4210118451","https://openalex.org/I52418104"],"apc_list":{"value":3390,"currency":"USD","value_usd":3390},"apc_paid":null,"fwci":4.9441,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.8863015,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"72","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.935699999332428,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.935699999332428,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.01600000075995922,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.014700000174343586,"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/multigrid-method","display_name":"Multigrid method","score":0.6650999784469604},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6301000118255615},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6219000220298767},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.54830002784729},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5077000260353088},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.47690001130104065},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.46230000257492065},{"id":"https://openalex.org/keywords/finite-difference-scheme","display_name":"Finite difference scheme","score":0.45239999890327454}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7781999707221985},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.6650999784469604},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6301000118255615},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6219000220298767},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.54830002784729},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5077000260353088},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5023999810218811},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.47690001130104065},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.46230000257492065},{"id":"https://openalex.org/C2988766672","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference scheme","level":2,"score":0.45239999890327454},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.44359999895095825},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.43970000743865967},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.42640000581741333},{"id":"https://openalex.org/C172100665","wikidata":"https://www.wikidata.org/wiki/Q7465774","display_name":"Thermal conduction","level":2,"score":0.39480000734329224},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.38040000200271606},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.3260999917984009},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32249999046325684},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3001999855041504},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.2865000069141388},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.2637999951839447},{"id":"https://openalex.org/C2780829570","wikidata":"https://www.wikidata.org/wiki/Q25113057","display_name":"Compact finite difference","level":3,"score":0.25029999017715454}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s12190-025-02739-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s12190-025-02739-y","pdf_url":null,"source":{"id":"https://openalex.org/S199913245","display_name":"Journal of Applied Mathematics and Computing","issn_l":"1226-0061","issn":["1226-0061","1229-9499","1229-9502","1598-5865","1865-2085"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics and Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5993942618370056,"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W132354056","https://openalex.org/W625917541","https://openalex.org/W1634777768","https://openalex.org/W1970212576","https://openalex.org/W1970659509","https://openalex.org/W1988634891","https://openalex.org/W1991377543","https://openalex.org/W1997542937","https://openalex.org/W2024516900","https://openalex.org/W2034976587","https://openalex.org/W2067290043","https://openalex.org/W2067809449","https://openalex.org/W2081544727","https://openalex.org/W2136631982","https://openalex.org/W2151781810","https://openalex.org/W2172050660","https://openalex.org/W2753152742","https://openalex.org/W2768550066","https://openalex.org/W2790598103","https://openalex.org/W2905383812","https://openalex.org/W2996231339","https://openalex.org/W3133745634","https://openalex.org/W3156003514","https://openalex.org/W3186026530","https://openalex.org/W4293110410","https://openalex.org/W4297054223","https://openalex.org/W4301596150","https://openalex.org/W4306154239","https://openalex.org/W4313623151","https://openalex.org/W4376623964","https://openalex.org/W4387137994","https://openalex.org/W4388991067","https://openalex.org/W4390669176","https://openalex.org/W4396827577"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2026-01-03T00:00:00"}