{"id":"https://openalex.org/W2041960787","doi":"https://doi.org/10.1080/10556780500286657","title":"Coupling quadrature and continuous Runge\u2013Kutta methods for optimal control problems","display_name":"Coupling quadrature and continuous Runge\u2013Kutta methods for optimal control problems","publication_year":2006,"publication_date":"2006-09-18","ids":{"openalex":"https://openalex.org/W2041960787","doi":"https://doi.org/10.1080/10556780500286657","mag":"2041960787"},"language":"en","primary_location":{"id":"doi:10.1080/10556780500286657","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556780500286657","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","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/A5038317749","display_name":"Fasma Diele","orcid":"https://orcid.org/0000-0002-4846-2795"},"institutions":[{"id":"https://openalex.org/I4210106125","display_name":"Istituto per le Applicazioni del Calcolo Mauro Picone","ror":"https://ror.org/00ygy3d85","country_code":"IT","type":"facility","lineage":["https://openalex.org/I4210106125","https://openalex.org/I4210155236"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"F. Diele","raw_affiliation_strings":["Instituto per le Applicazioni del Calcolo M. Picone, Sexione di Bari\u2014CNR, Via Amendola 122, 70126, Bari, Italy","Instituto per le Applicazioni del Calcolo M. Picone, Sexione di Bari\u2014CNR , Via Amendola 122, 70126, Bari, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto per le Applicazioni del Calcolo M. Picone, Sexione di Bari\u2014CNR, Via Amendola 122, 70126, Bari, Italy","institution_ids":["https://openalex.org/I4210106125"]},{"raw_affiliation_string":"Instituto per le Applicazioni del Calcolo M. Picone, Sexione di Bari\u2014CNR , Via Amendola 122, 70126, Bari, Italy","institution_ids":["https://openalex.org/I4210106125"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011065509","display_name":"Carmela Marangi","orcid":"https://orcid.org/0000-0002-6932-1430"},"institutions":[{"id":"https://openalex.org/I4210106125","display_name":"Istituto per le Applicazioni del Calcolo Mauro Picone","ror":"https://ror.org/00ygy3d85","country_code":"IT","type":"facility","lineage":["https://openalex.org/I4210106125","https://openalex.org/I4210155236"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"C. Marangi","raw_affiliation_strings":["Instituto per le Applicazioni del Calcolo M. Picone, Sexione di Bari\u2014CNR, Via Amendola 122, 70126, Bari, Italy","Instituto per le Applicazioni del Calcolo M. Picone, Sexione di Bari\u2014CNR , Via Amendola 122, 70126, Bari, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto per le Applicazioni del Calcolo M. Picone, Sexione di Bari\u2014CNR, Via Amendola 122, 70126, Bari, Italy","institution_ids":["https://openalex.org/I4210106125"]},{"raw_affiliation_string":"Instituto per le Applicazioni del Calcolo M. Picone, Sexione di Bari\u2014CNR , Via Amendola 122, 70126, Bari, Italy","institution_ids":["https://openalex.org/I4210106125"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022073474","display_name":"Stefania Ragni","orcid":"https://orcid.org/0000-0001-5864-8406"},"institutions":[{"id":"https://openalex.org/I5561750","display_name":"University of Bari Aldo Moro","ror":"https://ror.org/027ynra39","country_code":"IT","type":"education","lineage":["https://openalex.org/I5561750"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"S. Ragni","raw_affiliation_strings":["Facolt\u00e0 di Economia, Universit\u00e0 di Bari, Via Camillo Rosalba 56, 70100, Bari, Italy","Facolt\u00e0 di Economia , Universit\u00e0 di Bari , Via Camillo Rosalba 56, 70100, Bari, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Facolt\u00e0 di Economia, Universit\u00e0 di Bari, Via Camillo Rosalba 56, 70100, Bari, Italy","institution_ids":["https://openalex.org/I5561750"]},{"raw_affiliation_string":"Facolt\u00e0 di Economia , Universit\u00e0 di Bari , Via Camillo Rosalba 56, 70100, Bari, Italy","institution_ids":["https://openalex.org/I5561750"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5038317749"],"corresponding_institution_ids":["https://openalex.org/I4210106125"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.12323846,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"21","issue":"6","first_page":"961","last_page":"975"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9842000007629395,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9842000007629395,"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/T13855","display_name":"Aerospace Engineering and Control Systems","score":0.9754999876022339,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.939300000667572,"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/discretization","display_name":"Discretization","score":0.7995786666870117},{"id":"https://openalex.org/keywords/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.7743463516235352},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.7236219644546509},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.5902711749076843},{"id":"https://openalex.org/keywords/nystr\u00f6m-method","display_name":"Nystr\u00f6m method","score":0.5749469995498657},{"id":"https://openalex.org/keywords/matlab","display_name":"MATLAB","score":0.56874680519104},{"id":"https://openalex.org/keywords/coupling","display_name":"Coupling (piping)","score":0.5150415897369385},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5026845932006836},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48325854539871216},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.4652036130428314},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.42801767587661743},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.4265308380126953},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3855714499950409},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37512484192848206},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35791221261024475},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.2399292290210724},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12925377488136292}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7995786666870117},{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.7743463516235352},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.7236219644546509},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5902711749076843},{"id":"https://openalex.org/C48265008","wikidata":"https://www.wikidata.org/wiki/Q7071295","display_name":"Nystr\u00f6m method","level":3,"score":0.5749469995498657},{"id":"https://openalex.org/C2780365114","wikidata":"https://www.wikidata.org/wiki/Q169478","display_name":"MATLAB","level":2,"score":0.56874680519104},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.5150415897369385},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5026845932006836},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48325854539871216},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.4652036130428314},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.42801767587661743},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4265308380126953},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3855714499950409},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37512484192848206},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35791221261024475},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.2399292290210724},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12925377488136292},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/10556780500286657","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556780500286657","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"},{"id":"pmh:oai:iris.unife.it:11392/2336456","is_oa":false,"landing_page_url":"http://hdl.handle.net/11392/2336456","pdf_url":null,"source":{"id":"https://openalex.org/S4306400369","display_name":"Institutional Research Information System University of Ferrara (University of Ferrara)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I201324441","host_organization_name":"University of Ferrara","host_organization_lineage":["https://openalex.org/I201324441"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320310371","display_name":"University of Otago","ror":"https://ror.org/01jmxt844"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W82600489","https://openalex.org/W97838378","https://openalex.org/W641945295","https://openalex.org/W1483556071","https://openalex.org/W1550341792","https://openalex.org/W1985249384","https://openalex.org/W2001222787","https://openalex.org/W2007255973","https://openalex.org/W2048717288","https://openalex.org/W2165126234","https://openalex.org/W2314359380","https://openalex.org/W2561675875","https://openalex.org/W2787494143","https://openalex.org/W4249558666"],"related_works":["https://openalex.org/W3178131028","https://openalex.org/W2083621394","https://openalex.org/W1963845699","https://openalex.org/W2035232447","https://openalex.org/W1561827849","https://openalex.org/W4237740072","https://openalex.org/W2056088350","https://openalex.org/W2243194968","https://openalex.org/W2144321310","https://openalex.org/W2001419904"],"abstract_inverted_index":{"This":[0],"article":[1],"deals":[2],"with":[3,101],"the":[4,20,33,80,92,102,119],"numerical":[5,69],"solution":[6,47],"of":[7,35,45,79,94,110,118],"optimal":[8,125],"control":[9],"problems":[10,89],"for":[11,124],"ordinary":[12],"differential":[13],"equations.":[14],"The":[15,43,77,122],"approach":[16],"is":[17],"based":[18],"on":[19,86],"coupling":[21,54],"between":[22],"quadrature":[23],"rules":[24],"and":[25,29,39,53,114],"continuous":[26],"Runge\u2013Kutta":[27,106],"solvers,":[28],"it":[30],"lies":[31],"in":[32,91,108,133],"framework":[34],"direct":[36],"optimization":[37,120],"methods":[38,61],"recursive":[40],"discretization":[41],"techniques.":[42],"analysis":[44],"discrete":[46],"accuracy":[48,66],"has":[49,83,127],"been":[50,84,99,128],"carried":[51],"out":[52],"criteria":[55],"are":[56,71],"established":[57],"to":[58,74],"have":[59,98],"global":[60],"featured":[62],"by":[63,104,130],"a":[64],"given":[65],"order.":[67],"Consequently,":[68],"schemes":[70,82],"built":[72],"up":[73],"high":[75],"orders.":[76],"effectiveness":[78],"proposed":[81],"validated":[85],"several":[87],"test":[88],"arising":[90],"field":[93],"economic":[95],"applications.":[96],"Results":[97],"compared":[100],"ones":[103],"classical":[105],"methods,":[107],"terms":[109],"single":[111],"function":[112],"evaluations":[113],"average":[115],"CPU":[116],"time":[117],"process.":[121],"search":[123],"solutions":[126],"performed":[129],"standard":[131],"algorithms":[132],"Matlab":[134],"environment.":[135]},"counts_by_year":[{"year":2018,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
