{"id":"https://openalex.org/W2092508320","doi":"https://doi.org/10.1080/0020716031000070625","title":"A Chebyshev Finite Difference Method For Solving A Class Of Optimal Control Problems","display_name":"A Chebyshev Finite Difference Method For Solving A Class Of Optimal Control Problems","publication_year":2003,"publication_date":"2003-07-01","ids":{"openalex":"https://openalex.org/W2092508320","doi":"https://doi.org/10.1080/0020716031000070625","mag":"2092508320"},"language":"en","primary_location":{"id":"doi:10.1080/0020716031000070625","is_oa":false,"landing_page_url":"https://doi.org/10.1080/0020716031000070625","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"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":"International Journal of Computer Mathematics","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/A5001991582","display_name":"M. El-Kady","orcid":"https://orcid.org/0000-0002-4644-6804"},"institutions":[{"id":"https://openalex.org/I189575948","display_name":"South Valley University","ror":"https://ror.org/00jxshx33","country_code":"EG","type":"education","lineage":["https://openalex.org/I189575948"]}],"countries":["EG"],"is_corresponding":true,"raw_author_name":"M. El-Kady","raw_affiliation_strings":["Department of Mathematics, Faculty of Science , South Valley University , Aswan,  Egypt","Department of Mathematics Faculty of Science South Valley University Aswan, Egypt"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science , South Valley University , Aswan,  Egypt","institution_ids":["https://openalex.org/I189575948"]},{"raw_affiliation_string":"Department of Mathematics Faculty of Science South Valley University Aswan, Egypt","institution_ids":["https://openalex.org/I189575948"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5001991582"],"corresponding_institution_ids":["https://openalex.org/I189575948"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.1968292,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"80","issue":"7","first_page":"883","last_page":"895"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9984999895095825,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9984999895095825,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9980999827384949,"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":0.9980000257492065,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/chebyshev-pseudospectral-method","display_name":"Chebyshev pseudospectral method","score":0.8706340193748474},{"id":"https://openalex.org/keywords/chebyshev-filter","display_name":"Chebyshev filter","score":0.8648216724395752},{"id":"https://openalex.org/keywords/chebyshev-iteration","display_name":"Chebyshev iteration","score":0.7868868112564087},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7374662756919861},{"id":"https://openalex.org/keywords/chebyshev-equation","display_name":"Chebyshev equation","score":0.7239487767219543},{"id":"https://openalex.org/keywords/chebyshev-nodes","display_name":"Chebyshev nodes","score":0.6674366593360901},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.6527125835418701},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5480773448944092},{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":0.49755385518074036},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49575909972190857},{"id":"https://openalex.org/keywords/approximation-theory","display_name":"Approximation theory","score":0.4829558730125427},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.4742808938026428},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.4459449350833893},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.41295963525772095},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22735506296157837},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1645756959915161},{"id":"https://openalex.org/keywords/classical-orthogonal-polynomials","display_name":"Classical orthogonal polynomials","score":0.05955475568771362}],"concepts":[{"id":"https://openalex.org/C122107654","wikidata":"https://www.wikidata.org/wiki/Q5089017","display_name":"Chebyshev pseudospectral method","level":5,"score":0.8706340193748474},{"id":"https://openalex.org/C21424316","wikidata":"https://www.wikidata.org/wiki/Q718621","display_name":"Chebyshev filter","level":2,"score":0.8648216724395752},{"id":"https://openalex.org/C196512905","wikidata":"https://www.wikidata.org/wiki/Q2457511","display_name":"Chebyshev iteration","level":3,"score":0.7868868112564087},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7374662756919861},{"id":"https://openalex.org/C142484921","wikidata":"https://www.wikidata.org/wiki/Q3890369","display_name":"Chebyshev equation","level":4,"score":0.7239487767219543},{"id":"https://openalex.org/C171326582","wikidata":"https://www.wikidata.org/wiki/Q1052508","display_name":"Chebyshev nodes","level":3,"score":0.6674366593360901},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.6527125835418701},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5480773448944092},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.49755385518074036},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49575909972190857},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.4829558730125427},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.4742808938026428},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4459449350833893},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41295963525772095},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22735506296157837},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1645756959915161},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.05955475568771362},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/0020716031000070625","is_oa":false,"landing_page_url":"https://doi.org/10.1080/0020716031000070625","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"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":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1537335979","https://openalex.org/W1587799944","https://openalex.org/W1623487976","https://openalex.org/W1967242138","https://openalex.org/W1971099220","https://openalex.org/W1983871555","https://openalex.org/W1997283008","https://openalex.org/W2001981441","https://openalex.org/W2018816843","https://openalex.org/W2029813969","https://openalex.org/W2035273811","https://openalex.org/W2049069909","https://openalex.org/W2051373638","https://openalex.org/W2052551315","https://openalex.org/W2053391813","https://openalex.org/W2056085001","https://openalex.org/W2080132051","https://openalex.org/W2082849992","https://openalex.org/W2108674204","https://openalex.org/W2127198082","https://openalex.org/W2318788438","https://openalex.org/W2334591577","https://openalex.org/W2410898212","https://openalex.org/W4246616525"],"related_works":["https://openalex.org/W2054912819","https://openalex.org/W2179563627","https://openalex.org/W1976132774","https://openalex.org/W88219822","https://openalex.org/W2039062045","https://openalex.org/W2018585115","https://openalex.org/W1866822838","https://openalex.org/W3196370734","https://openalex.org/W4233411521","https://openalex.org/W2011010098"],"abstract_inverted_index":{"A":[0],"new":[1],"Chebyshev":[2,20,35],"finite":[3],"difference":[4],"method":[5],"for":[6,37],"solving":[7],"class":[8],"of":[9,22,48],"optimal":[10],"control":[11],"problem":[12],"is":[13,17],"proposed.":[14],"The":[15,39],"algorithm":[16],"based":[18],"on":[19],"approximations":[21,36],"the":[23,30,43,49],"derivatives":[24],"arising":[25],"in":[26],"system":[27],"dynamics.":[28],"In":[29],"performance":[31],"index,":[32],"we":[33],"use":[34],"integration.":[38],"numerical":[40],"examples":[41],"illustrate":[42],"robustness,":[44],"accuracy":[45],"and":[46],"efficiency":[47],"proposed":[50],"technique.":[51]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
