{"id":"https://openalex.org/W2030771153","doi":"https://doi.org/10.1080/00207160412331296652","title":"A Chebyshev spectral method for time-varying two-point boundary-value and optimal control problems","display_name":"A Chebyshev spectral method for time-varying two-point boundary-value and optimal control problems","publication_year":2004,"publication_date":"2004-12-22","ids":{"openalex":"https://openalex.org/W2030771153","doi":"https://doi.org/10.1080/00207160412331296652","mag":"2030771153"},"language":"en","primary_location":{"id":"doi:10.1080/00207160412331296652","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160412331296652","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/A5048403129","display_name":"Gamal N. Elnagar","orcid":null},"institutions":[{"id":"https://openalex.org/I127845322","display_name":"University of South Carolina Upstate","ror":"https://ror.org/00t9hhv14","country_code":"US","type":"education","lineage":["https://openalex.org/I127845322"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Gamal Elnagar","raw_affiliation_strings":["Department of Mathematics and Computer Science , University of South Carolina Spartanburg , Spartanburg, SC, 29303,  USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science , University of South Carolina Spartanburg , Spartanburg, SC, 29303,  USA","institution_ids":["https://openalex.org/I127845322"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051662694","display_name":"Vasilis Zafiris","orcid":null},"institutions":[{"id":"https://openalex.org/I16277215","display_name":"University of Houston - Downtown","ror":"https://ror.org/05mj6fy81","country_code":"US","type":"education","lineage":["https://openalex.org/I16277215"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Vasilis Zafiris","raw_affiliation_strings":["Department of Mathematics and Computer Science , University of Houston-Downtown , One Main Street, Houston, TX, 77002,  USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science , University of Houston-Downtown , One Main Street, Houston, TX, 77002,  USA","institution_ids":["https://openalex.org/I16277215"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5048403129"],"corresponding_institution_ids":["https://openalex.org/I127845322"],"apc_list":null,"apc_paid":null,"fwci":0.5012,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.64330025,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"82","issue":"2","first_page":"193","last_page":"202"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9965999722480774,"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":0.9965999722480774,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9957000017166138,"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/T12206","display_name":"Vibration and Dynamic Analysis","score":0.9782999753952026,"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/mathematics","display_name":"Mathematics","score":0.7940301895141602},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5697184801101685},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5681642889976501},{"id":"https://openalex.org/keywords/chebyshev-filter","display_name":"Chebyshev filter","score":0.5421865582466125},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5305578708648682},{"id":"https://openalex.org/keywords/chebyshev-iteration","display_name":"Chebyshev iteration","score":0.5252030491828918},{"id":"https://openalex.org/keywords/chebyshev-nodes","display_name":"Chebyshev nodes","score":0.496662437915802},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.465657502412796},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4613149166107178},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4536806643009186},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4387654662132263},{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":0.4347558617591858},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24845460057258606},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15117233991622925}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7940301895141602},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5697184801101685},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5681642889976501},{"id":"https://openalex.org/C21424316","wikidata":"https://www.wikidata.org/wiki/Q718621","display_name":"Chebyshev filter","level":2,"score":0.5421865582466125},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5305578708648682},{"id":"https://openalex.org/C196512905","wikidata":"https://www.wikidata.org/wiki/Q2457511","display_name":"Chebyshev iteration","level":3,"score":0.5252030491828918},{"id":"https://openalex.org/C171326582","wikidata":"https://www.wikidata.org/wiki/Q1052508","display_name":"Chebyshev nodes","level":3,"score":0.496662437915802},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.465657502412796},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4613149166107178},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4536806643009186},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4387654662132263},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.4347558617591858},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24845460057258606},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15117233991622925},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160412331296652","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160412331296652","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":7,"referenced_works":["https://openalex.org/W1971647756","https://openalex.org/W2025665965","https://openalex.org/W2039091159","https://openalex.org/W2050613592","https://openalex.org/W2129022762","https://openalex.org/W4295133295","https://openalex.org/W4298060601"],"related_works":["https://openalex.org/W2021099221","https://openalex.org/W2112919228","https://openalex.org/W2136992695","https://openalex.org/W2054912819","https://openalex.org/W2039550572","https://openalex.org/W2025308149","https://openalex.org/W2345201752","https://openalex.org/W2090151895","https://openalex.org/W2106962382","https://openalex.org/W2074316639"],"abstract_inverted_index":{"A":[0],"numerical":[1],"method":[2,17,43,78],"for":[3],"solving":[4],"two-point":[5,36,62],"boundary-value":[6],"problems":[7,38],"with":[8,39],"time-varying":[9,40,54],"coefficients":[10],"is":[11,18,79],"presented":[12],"in":[13],"this":[14],"paper.":[15],"The":[16,42,61,77],"based":[19],"on":[20],"constructing":[21],"the":[22,32,49,66,94],"Nth":[23],"degree":[24],"polynomial":[25],"interpolation":[26],"using":[27],"Chebyshev\u2019s":[28],"nodes":[29],"to":[30,47,57,92],"approximate":[31],"solution":[33],"of":[34,52,96],"linear":[35,53],"value":[37,63],"coefficients.":[41],"can":[44],"be":[45],"applied":[46],"obtain":[48],"optimal":[50,67],"control":[51,68],"systems":[55],"subject":[56],"quadratic":[58],"cost":[59],"criteria.":[60],"problem":[64,69],"and":[65,81,83],"are":[70,90],"thereby":[71],"transformed":[72],"into":[73],"a":[74],"programming":[75],"problem.":[76],"simple":[80],"efficient,":[82],"yields":[84],"very":[85],"accurate":[86],"results.":[87],"Illustrative":[88],"examples":[89],"included":[91],"demonstrate":[93],"accuracy":[95],"method.":[97]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}