{"id":"https://openalex.org/W266968240","doi":"https://doi.org/10.1080/00207169208804053","title":"Modified newton\u2013cotes formulae for numerical quadrature of oscillatory integrals with two independent variable frequencies","display_name":"Modified newton\u2013cotes formulae for numerical quadrature of oscillatory integrals with two independent variable frequencies","publication_year":1992,"publication_date":"1992-01-01","ids":{"openalex":"https://openalex.org/W266968240","doi":"https://doi.org/10.1080/00207169208804053","mag":"266968240"},"language":"en","primary_location":{"id":"doi:10.1080/00207169208804053","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169208804053","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","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"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/A5088494720","display_name":"Maarten Van Daele","orcid":"https://orcid.org/0000-0002-8530-4438"},"institutions":[{"id":"https://openalex.org/I4210142349","display_name":"Koninklijk Nederlands Genootschap voor Fysiotherapie","ror":"https://ror.org/04946nn35","country_code":"NL","type":"other","lineage":["https://openalex.org/I4210142349"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"M. Van Daele","raw_affiliation_strings":["Laboratorium voor Numerieke Wiskunde en Informatica, Rijksuniversiteit-Gent, Krijgslaan 281-S9, Gent, B9000, Belgium","Laboratorium voor Numerieke Wiskunde en Informatica , Rijksuniversiteit-Gent , Krijgslaan 281-S9, Gent, B9000, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratorium voor Numerieke Wiskunde en Informatica, Rijksuniversiteit-Gent, Krijgslaan 281-S9, Gent, B9000, Belgium","institution_ids":["https://openalex.org/I4210142349"]},{"raw_affiliation_string":"Laboratorium voor Numerieke Wiskunde en Informatica , Rijksuniversiteit-Gent , Krijgslaan 281-S9, Gent, B9000, Belgium","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109967168","display_name":"H. De Meyer","orcid":null},"institutions":[{"id":"https://openalex.org/I4210142349","display_name":"Koninklijk Nederlands Genootschap voor Fysiotherapie","ror":"https://ror.org/04946nn35","country_code":"NL","type":"other","lineage":["https://openalex.org/I4210142349"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"H. De Meyer","raw_affiliation_strings":["Laboratorium voor Numerieke Wiskunde en Informatica, Rijksuniversiteit-Gent, Krijgslaan 281-S9, Gent, B9000, Belgium","Laboratorium voor Numerieke Wiskunde en Informatica , Rijksuniversiteit-Gent , Krijgslaan 281-S9, Gent, B9000, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratorium voor Numerieke Wiskunde en Informatica, Rijksuniversiteit-Gent, Krijgslaan 281-S9, Gent, B9000, Belgium","institution_ids":["https://openalex.org/I4210142349"]},{"raw_affiliation_string":"Laboratorium voor Numerieke Wiskunde en Informatica , Rijksuniversiteit-Gent , Krijgslaan 281-S9, Gent, B9000, Belgium","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036599342","display_name":"G. Vanden Berghe","orcid":"https://orcid.org/0000-0002-7215-9446"},"institutions":[{"id":"https://openalex.org/I4210142349","display_name":"Koninklijk Nederlands Genootschap voor Fysiotherapie","ror":"https://ror.org/04946nn35","country_code":"NL","type":"other","lineage":["https://openalex.org/I4210142349"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"G. Vanden Berghe","raw_affiliation_strings":["Laboratorium voor Numerieke Wiskunde en Informatica, Rijksuniversiteit-Gent, Krijgslaan 281-S9, Gent, B9000, Belgium","Laboratorium voor Numerieke Wiskunde en Informatica , Rijksuniversiteit-Gent , Krijgslaan 281-S9, Gent, B9000, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratorium voor Numerieke Wiskunde en Informatica, Rijksuniversiteit-Gent, Krijgslaan 281-S9, Gent, B9000, Belgium","institution_ids":["https://openalex.org/I4210142349"]},{"raw_affiliation_string":"Laboratorium voor Numerieke Wiskunde en Informatica , Rijksuniversiteit-Gent , Krijgslaan 281-S9, Gent, B9000, Belgium","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210142349"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.01912929,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"42","issue":"1-2","first_page":"83","last_page":"97"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9927999973297119,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9927999973297119,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9907000064849854,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.989799976348877,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/mathematics","display_name":"Mathematics","score":0.8581916093826294},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.7035130262374878},{"id":"https://openalex.org/keywords/gauss\u2013kronrod-quadrature-formula","display_name":"Gauss\u2013Kronrod quadrature formula","score":0.6922926306724548},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.6608776450157166},{"id":"https://openalex.org/keywords/tanh-sinh-quadrature","display_name":"Tanh-sinh quadrature","score":0.6370052099227905},{"id":"https://openalex.org/keywords/gauss\u2013jacobi-quadrature","display_name":"Gauss\u2013Jacobi quadrature","score":0.5846174359321594},{"id":"https://openalex.org/keywords/clenshaw\u2013curtis-quadrature","display_name":"Clenshaw\u2013Curtis quadrature","score":0.5714517831802368},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5559056997299194},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5373603105545044},{"id":"https://openalex.org/keywords/truncation-error","display_name":"Truncation error","score":0.5320806503295898},{"id":"https://openalex.org/keywords/divided-differences","display_name":"Divided differences","score":0.46015575528144836},{"id":"https://openalex.org/keywords/polynomial-interpolation","display_name":"Polynomial interpolation","score":0.45602792501449585},{"id":"https://openalex.org/keywords/gaussian-quadrature","display_name":"Gaussian quadrature","score":0.44284969568252563},{"id":"https://openalex.org/keywords/truncation","display_name":"Truncation (statistics)","score":0.42607763409614563},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.41953879594802856},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.40406808257102966},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40229490399360657},{"id":"https://openalex.org/keywords/linear-interpolation","display_name":"Linear interpolation","score":0.32829636335372925},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19807901978492737},{"id":"https://openalex.org/keywords/nystr\u00f6m-method","display_name":"Nystr\u00f6m method","score":0.14777016639709473},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.14733123779296875}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8581916093826294},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.7035130262374878},{"id":"https://openalex.org/C14103991","wikidata":"https://www.wikidata.org/wiki/Q5527852","display_name":"Gauss\u2013Kronrod quadrature formula","level":4,"score":0.6922926306724548},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.6608776450157166},{"id":"https://openalex.org/C162046254","wikidata":"https://www.wikidata.org/wiki/Q7683194","display_name":"Tanh-sinh quadrature","level":5,"score":0.6370052099227905},{"id":"https://openalex.org/C54691486","wikidata":"https://www.wikidata.org/wiki/Q5527851","display_name":"Gauss\u2013Jacobi quadrature","level":5,"score":0.5846174359321594},{"id":"https://openalex.org/C172657837","wikidata":"https://www.wikidata.org/wiki/Q5131618","display_name":"Clenshaw\u2013Curtis quadrature","level":5,"score":0.5714517831802368},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5559056997299194},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5373603105545044},{"id":"https://openalex.org/C104942944","wikidata":"https://www.wikidata.org/wiki/Q3434686","display_name":"Truncation error","level":2,"score":0.5320806503295898},{"id":"https://openalex.org/C183554904","wikidata":"https://www.wikidata.org/wiki/Q2993265","display_name":"Divided differences","level":2,"score":0.46015575528144836},{"id":"https://openalex.org/C88080468","wikidata":"https://www.wikidata.org/wiki/Q637347","display_name":"Polynomial interpolation","level":4,"score":0.45602792501449585},{"id":"https://openalex.org/C167196314","wikidata":"https://www.wikidata.org/wiki/Q767680","display_name":"Gaussian quadrature","level":4,"score":0.44284969568252563},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.42607763409614563},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.41953879594802856},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.40406808257102966},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40229490399360657},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.32829636335372925},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19807901978492737},{"id":"https://openalex.org/C48265008","wikidata":"https://www.wikidata.org/wiki/Q7071295","display_name":"Nystr\u00f6m method","level":3,"score":0.14777016639709473},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.14733123779296875},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00207169208804053","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169208804053","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","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"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"},{"id":"pmh:oai:archive.ugent.be:205195","is_oa":false,"landing_page_url":"http://hdl.handle.net/1854/LU-205195","pdf_url":null,"source":{"id":"https://openalex.org/S4306400478","display_name":"Ghent University Academic Bibliography (Ghent University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I32597200","host_organization_name":"Ghent University","host_organization_lineage":["https://openalex.org/I32597200"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 0020-7160","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1996453810","https://openalex.org/W2003923484","https://openalex.org/W2010311824","https://openalex.org/W2029544476","https://openalex.org/W2060238526","https://openalex.org/W2073732659","https://openalex.org/W2084975323","https://openalex.org/W2090344516","https://openalex.org/W2109537209","https://openalex.org/W2142821382","https://openalex.org/W2149109834","https://openalex.org/W2154951648","https://openalex.org/W2463002925","https://openalex.org/W2574741566","https://openalex.org/W4299112371"],"related_works":["https://openalex.org/W2289189603","https://openalex.org/W1661554543","https://openalex.org/W4390128132","https://openalex.org/W2148120208","https://openalex.org/W2049479394","https://openalex.org/W4317584040","https://openalex.org/W2765175526","https://openalex.org/W4387847482","https://openalex.org/W2520857016","https://openalex.org/W3115048450"],"abstract_inverted_index":{"It":[0],"is":[1,20,79,96,107,114,143,160],"shown":[2],"how":[3],"a":[4,10,21,33,89,141],"function":[5,16,70],"can":[6],"be":[7],"approximated":[8],"in":[9,45,81,116],"unique":[11],"way":[12],"by":[13],"an":[14],"interpolation":[15,69,88],"fn":[17,41,71],"(x)":[18],"which":[19,124],"linear":[22],"combination":[23],"of":[24,35,67,87,91],"cos":[25,29],"kx,":[26,28],"sin":[27,31],"k\u2032x,":[30],"k\u2032xand":[32],"polynomial":[34],"{n\u2013":[36],"4)th":[37],"degree,":[38],"such":[39,154],"that":[40,155],"coincides":[42],"with":[43,104],"f(x)":[44],"(n":[46],"+":[47],"1)":[48],"equidistant":[49],"points,":[50],"and":[51,74,98,119,152],"whereby":[52],"kand":[53],"k\u2032are":[54],"two":[55],"arbitrary":[56],"real,":[57],"purely":[58],"imaginary":[59],"or":[60],"complex":[61],"conjugate":[62],"parameters.":[63],"Several":[64],"equivalent":[65],"expressions":[66],"the":[68,76,99,110,129,149,156],"are":[72,122,132],"given,":[73],"also":[75],"error":[77,102,159],"term":[78],"derived":[80,123],"closed":[82],"form.":[83],"With":[84],"this":[85],"type":[86],"set":[90],"modified":[92],"Newton\u2013Cotes":[93],"quadrature":[94,112],"rules":[95,106],"established":[97,144],"total":[100,157],"truncation":[101,158],"associated":[103],"these":[105],"discussed.":[108],"Subsequently,":[109],"five-point":[111],"rule":[113],"treated":[115],"full":[117],"detail":[118],"several":[120],"formulae":[121,131],"facilitate":[125],"numerical":[126,137],"computation.":[127],"Finally,":[128],"proposed":[130],"implemented":[133],"for":[134,145],"certain":[135],"illustrative":[136],"examples.":[138],"In":[139],"particular,":[140],"technique":[142],"attributing":[146],"values":[147],"to":[148],"parameters":[150],"k":[151],"k\u2032":[153],"minimized.":[161]},"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-15T07:11:24.734988","created_date":"2025-10-10T00:00:00"}
