{"id":"https://openalex.org/W4408296768","doi":"https://doi.org/10.3390/a18030153","title":"The Euler-Type Universal Numerical Integrator (E-TUNI) with Backward Integration","display_name":"The Euler-Type Universal Numerical Integrator (E-TUNI) with Backward Integration","publication_year":2025,"publication_date":"2025-03-08","ids":{"openalex":"https://openalex.org/W4408296768","doi":"https://doi.org/10.3390/a18030153"},"language":"en","primary_location":{"id":"doi:10.3390/a18030153","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a18030153","pdf_url":"https://www.mdpi.com/1999-4893/18/3/153/pdf?version=1741603319","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"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":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/18/3/153/pdf?version=1741603319","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071121096","display_name":"Paulo Marcelo Tasinaffo","orcid":"https://orcid.org/0000-0001-7069-8430"},"institutions":[{"id":"https://openalex.org/I107428990","display_name":"Instituto Tecnol\u00f3gico de Aeron\u00e1utica","ror":"https://ror.org/05vh67662","country_code":"BR","type":"education","lineage":["https://openalex.org/I107428990"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Paulo M. Tasinaffo","raw_affiliation_strings":["Instituto Tecnol\u00f3gico de Aeron\u00e1utica (ITA), S\u00e3o Jos\u00e9 dos Campos 12228-900, SP, Brazil"],"affiliations":[{"raw_affiliation_string":"Instituto Tecnol\u00f3gico de Aeron\u00e1utica (ITA), S\u00e3o Jos\u00e9 dos Campos 12228-900, SP, Brazil","institution_ids":["https://openalex.org/I107428990"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013523163","display_name":"Gild\u00e1rcio Sousa Gon\u00e7alves","orcid":"https://orcid.org/0000-0003-0932-9171"},"institutions":[{"id":"https://openalex.org/I107428990","display_name":"Instituto Tecnol\u00f3gico de Aeron\u00e1utica","ror":"https://ror.org/05vh67662","country_code":"BR","type":"education","lineage":["https://openalex.org/I107428990"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Gild\u00e1rcio S. Gon\u00e7alves","raw_affiliation_strings":["Instituto Tecnol\u00f3gico de Aeron\u00e1utica (ITA), S\u00e3o Jos\u00e9 dos Campos 12228-900, SP, Brazil"],"affiliations":[{"raw_affiliation_string":"Instituto Tecnol\u00f3gico de Aeron\u00e1utica (ITA), S\u00e3o Jos\u00e9 dos Campos 12228-900, SP, Brazil","institution_ids":["https://openalex.org/I107428990"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030850691","display_name":"Johnny Marques","orcid":"https://orcid.org/0000-0002-1551-435X"},"institutions":[{"id":"https://openalex.org/I107428990","display_name":"Instituto Tecnol\u00f3gico de Aeron\u00e1utica","ror":"https://ror.org/05vh67662","country_code":"BR","type":"education","lineage":["https://openalex.org/I107428990"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Johnny C. Marques","raw_affiliation_strings":["Instituto Tecnol\u00f3gico de Aeron\u00e1utica (ITA), S\u00e3o Jos\u00e9 dos Campos 12228-900, SP, Brazil"],"affiliations":[{"raw_affiliation_string":"Instituto Tecnol\u00f3gico de Aeron\u00e1utica (ITA), S\u00e3o Jos\u00e9 dos Campos 12228-900, SP, Brazil","institution_ids":["https://openalex.org/I107428990"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014821780","display_name":"Luiz Alberto Vieira Dias","orcid":"https://orcid.org/0000-0001-5958-8011"},"institutions":[{"id":"https://openalex.org/I107428990","display_name":"Instituto Tecnol\u00f3gico de Aeron\u00e1utica","ror":"https://ror.org/05vh67662","country_code":"BR","type":"education","lineage":["https://openalex.org/I107428990"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Luiz A. V. Dias","raw_affiliation_strings":["Instituto Tecnol\u00f3gico de Aeron\u00e1utica (ITA), S\u00e3o Jos\u00e9 dos Campos 12228-900, SP, Brazil"],"affiliations":[{"raw_affiliation_string":"Instituto Tecnol\u00f3gico de Aeron\u00e1utica (ITA), S\u00e3o Jos\u00e9 dos Campos 12228-900, SP, Brazil","institution_ids":["https://openalex.org/I107428990"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063426225","display_name":"Adilson Marques da Cunha","orcid":"https://orcid.org/0000-0003-2399-5066"},"institutions":[{"id":"https://openalex.org/I107428990","display_name":"Instituto Tecnol\u00f3gico de Aeron\u00e1utica","ror":"https://ror.org/05vh67662","country_code":"BR","type":"education","lineage":["https://openalex.org/I107428990"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Adilson M. da Cunha","raw_affiliation_strings":["Instituto Tecnol\u00f3gico de Aeron\u00e1utica (ITA), S\u00e3o Jos\u00e9 dos Campos 12228-900, SP, Brazil"],"affiliations":[{"raw_affiliation_string":"Instituto Tecnol\u00f3gico de Aeron\u00e1utica (ITA), S\u00e3o Jos\u00e9 dos Campos 12228-900, SP, Brazil","institution_ids":["https://openalex.org/I107428990"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5071121096"],"corresponding_institution_ids":["https://openalex.org/I107428990"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":4.9698,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.94117057,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"18","issue":"3","first_page":"153","last_page":"153"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9876999855041504,"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/T11236","display_name":"Control Systems and Identification","score":0.9824000000953674,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/integrator","display_name":"Integrator","score":0.8312891721725464},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.7114079594612122},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.6434570550918579},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5683416128158569},{"id":"https://openalex.org/keywords/semi-implicit-euler-method","display_name":"Semi-implicit Euler method","score":0.5267069935798645},{"id":"https://openalex.org/keywords/backward-euler-method","display_name":"Backward Euler method","score":0.4599977433681488},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.41632962226867676},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39068740606307983},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3831101655960083},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35202687978744507},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3468396067619324},{"id":"https://openalex.org/keywords/euler-equations","display_name":"Euler equations","score":0.15721604228019714},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.09002849459648132}],"concepts":[{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.8312891721725464},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.7114079594612122},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.6434570550918579},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5683416128158569},{"id":"https://openalex.org/C93082080","wikidata":"https://www.wikidata.org/wiki/Q5475314","display_name":"Semi-implicit Euler method","level":4,"score":0.5267069935798645},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.4599977433681488},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.41632962226867676},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39068740606307983},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3831101655960083},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35202687978744507},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3468396067619324},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.15721604228019714},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.09002849459648132},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"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/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/a18030153","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a18030153","pdf_url":"https://www.mdpi.com/1999-4893/18/3/153/pdf?version=1741603319","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"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":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:3422bb5ac99f497c902b22a5a29cd4ca","is_oa":true,"landing_page_url":"https://doaj.org/article/3422bb5ac99f497c902b22a5a29cd4ca","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":"Algorithms, Vol 18, Iss 3, p 153 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/a18030153","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a18030153","pdf_url":"https://www.mdpi.com/1999-4893/18/3/153/pdf?version=1741603319","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"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":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4408296768.pdf"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W14243177","https://openalex.org/W1535260033","https://openalex.org/W1559282221","https://openalex.org/W1969705022","https://openalex.org/W1975100741","https://openalex.org/W1995341919","https://openalex.org/W2028847290","https://openalex.org/W2058419253","https://openalex.org/W2097553780","https://openalex.org/W2103496339","https://openalex.org/W2137983211","https://openalex.org/W2138484437","https://openalex.org/W2139843466","https://openalex.org/W2152619728","https://openalex.org/W2155482699","https://openalex.org/W2516137357","https://openalex.org/W2570513205","https://openalex.org/W2743909828","https://openalex.org/W2883580648","https://openalex.org/W2955826308","https://openalex.org/W2998852813","https://openalex.org/W3099132019","https://openalex.org/W4404024834","https://openalex.org/W6633032110","https://openalex.org/W6726175428","https://openalex.org/W6874645218"],"related_works":["https://openalex.org/W2089955609","https://openalex.org/W2466040413","https://openalex.org/W4382053489","https://openalex.org/W2913079245","https://openalex.org/W2039299714","https://openalex.org/W2378504881","https://openalex.org/W2189596786","https://openalex.org/W2753480721","https://openalex.org/W2024540961","https://openalex.org/W4383710307"],"abstract_inverted_index":{"The":[0],"Euler-Type":[1],"Universal":[2],"Numerical":[3],"Integrator":[4],"(E-TUNI)":[5],"is":[6,40],"a":[7,13,68],"discrete":[8,44],"numerical":[9,16,96],"structure":[10],"that":[11],"couples":[12],"first-order":[14],"Euler-type":[15],"integrator":[17],"with":[18],"some":[19],"feed-forward":[20],"neural":[21],"network":[22],"architecture.":[23],"Thus,":[24,58],"E-TUNI":[25,66],"can":[26,52],"be":[27,53],"used":[28],"to":[29,64,72,91],"model":[30,39,73],"non-linear":[31,75,86],"dynamic":[32,76],"systems":[33],"when":[34],"the":[35,43,49,82,85,93,99],"real-world":[36],"plant\u2019s":[37],"analytical":[38],"unknown.":[41],"From":[42],"solution":[45],"provided":[46],"by":[47],"E-TUNI,":[48],"integration":[50,70],"process":[51],"either":[54],"forward":[55],"or":[56],"backward.":[57],"in":[59,67],"this":[60],"article,":[61],"we":[62],"intend":[63],"use":[65],"backward":[69],"framework":[71],"autonomous":[74],"systems.":[77],"Three":[78],"case":[79],"studies,":[80],"including":[81],"dynamics":[83],"of":[84,98],"inverted":[87],"pendulum,":[88],"were":[89],"developed":[90],"verify":[92],"computational":[94],"and":[95],"validation":[97],"proposed":[100],"model.":[101]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}