{"id":"https://openalex.org/W1993016870","doi":"https://doi.org/10.1080/00207161003631877","title":"Analysis of a Chebyshev-based backward differentiation formulae and relation with Runge\u2013Kutta collocation methods","display_name":"Analysis of a Chebyshev-based backward differentiation formulae and relation with Runge\u2013Kutta collocation methods","publication_year":2010,"publication_date":"2010-12-13","ids":{"openalex":"https://openalex.org/W1993016870","doi":"https://doi.org/10.1080/00207161003631877","mag":"1993016870"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207161003631877","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_indexed_in_scopus":true,"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":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-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/A5005180650","display_name":"Higinio Ramos","orcid":"https://orcid.org/0000-0003-2791-6230"},"institutions":[],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Higinio Ramos","raw_affiliation_strings":["Escuela Politecnica Superior, Zamora, Spain#TAB#"],"affiliations":[{"raw_affiliation_string":"Escuela Politecnica Superior, Zamora, Spain#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113650350","display_name":"R. Garc\u00eda-Rubio","orcid":null},"institutions":[{"id":"https://openalex.org/I130194489","display_name":"University of Alicante","ror":"https://ror.org/05t8bcz72","country_code":"ES","type":"funder","lineage":["https://openalex.org/I130194489"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"R. Garc\u00eda-Rubio","raw_affiliation_strings":["Departmento de Matematica Aplicada, Universidad de Alicante, Alicante, Spain#TAB#"],"affiliations":[{"raw_affiliation_string":"Departmento de Matematica Aplicada, Universidad de Alicante, Alicante, Spain#TAB#","institution_ids":["https://openalex.org/I130194489"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.836,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":7,"citation_normalized_percentile":{"value":0.709459,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":82,"max":83},"biblio":{"volume":"88","issue":"3","first_page":"555","last_page":"577"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9999,"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":0.9999,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9965,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9929,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.82898474},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.6973936},{"id":"https://openalex.org/keywords/orthogonal-collocation","display_name":"Orthogonal collocation","score":0.44786328}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.89947224},{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.82898474},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.6973936},{"id":"https://openalex.org/C161794534","wikidata":"https://www.wikidata.org/wiki/Q177493","display_name":"Gauss","level":2,"score":0.69512445},{"id":"https://openalex.org/C21424316","wikidata":"https://www.wikidata.org/wiki/Q718621","display_name":"Chebyshev filter","level":2,"score":0.6631836},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.616904},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5571609},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.54985964},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.49928093},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.49651438},{"id":"https://openalex.org/C114609681","wikidata":"https://www.wikidata.org/wiki/Q24839227","display_name":"Orthogonal collocation","level":5,"score":0.44786328},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43433475},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.43052167},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3733277},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62649853","wikidata":"https://www.wikidata.org/wiki/Q199687","display_name":"Remote sensing","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207161003631877","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_indexed_in_scopus":true,"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":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":46,"referenced_works":["https://openalex.org/W140628048","https://openalex.org/W1509923322","https://openalex.org/W1543750907","https://openalex.org/W1655797795","https://openalex.org/W1967283925","https://openalex.org/W1968512837","https://openalex.org/W1971438134","https://openalex.org/W1980288255","https://openalex.org/W1981115560","https://openalex.org/W1988646016","https://openalex.org/W1995504856","https://openalex.org/W1997036967","https://openalex.org/W2000374946","https://openalex.org/W2005653523","https://openalex.org/W2007665571","https://openalex.org/W2007831744","https://openalex.org/W2016358317","https://openalex.org/W2021066039","https://openalex.org/W2023171195","https://openalex.org/W2023173294","https://openalex.org/W2029290244","https://openalex.org/W2039880089","https://openalex.org/W2045181815","https://openalex.org/W2046754080","https://openalex.org/W2057184888","https://openalex.org/W2059632797","https://openalex.org/W2059998776","https://openalex.org/W2066969405","https://openalex.org/W2077221255","https://openalex.org/W2080036729","https://openalex.org/W2083915368","https://openalex.org/W2098533238","https://openalex.org/W2104946123","https://openalex.org/W2134198662","https://openalex.org/W2154876043","https://openalex.org/W2155809947","https://openalex.org/W222318538","https://openalex.org/W2335697030","https://openalex.org/W2484971506","https://openalex.org/W2529992474","https://openalex.org/W3209416867","https://openalex.org/W3214781692","https://openalex.org/W4254246953","https://openalex.org/W4255754126","https://openalex.org/W569671260","https://openalex.org/W585625230"],"related_works":["https://openalex.org/W4206513033","https://openalex.org/W2890254931","https://openalex.org/W2791210196","https://openalex.org/W2384941625","https://openalex.org/W2296924041","https://openalex.org/W2132514189","https://openalex.org/W1972581143","https://openalex.org/W1843663759","https://openalex.org/W1562832873","https://openalex.org/W1482343169"],"abstract_inverted_index":{"The":[0],"construction":[1],"of":[2,5,21,24,32,55,71],"a":[3],"class":[4,63],"backward":[6],"differentiation":[7],"formulae":[8],"based":[9],"on":[10],"intra-step":[11],"Chebyshev\u2013Gauss\u2013Lobatto":[12,87],"nodal":[13],"points,":[14],"suitable":[15],"for":[16,41,46],"the":[17,81,86],"approximate":[18],"numerical":[19],"integration":[20],"initial-value":[22],"problems":[23],"first-order":[25],"ordinary":[26],"differential":[27],"equations,":[28],"is":[29],"presented.":[30],"Formulae":[31],"this":[33,62,69],"new":[34],"family":[35,70],"are":[36,52,83],"A":[37],"0-stable":[38],"and":[39,49,58],"L(\u03b1)-stable":[40],"any":[42],"orders,":[43],"and,":[44],"particularly,":[45],"orders":[47],"1":[48],"2":[50],"they":[51],"L-stable.":[53],"Regions":[54],"absolute":[56],"stability":[57,59],"measures":[60],"make":[61],"very":[64],"promising.":[65],"We":[66],"prove":[67],"that":[68],"methods":[72,79],"may":[73],"be":[74],"considered":[75],"as":[76],"Runge\u2013Kutta":[77],"collocation":[78],"where":[80],"abscissae":[82],"obtained":[84],"from":[85],"points.":[88]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W1993016870","counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1}],"updated_date":"2025-03-22T05:28:56.035284","created_date":"2016-06-24"}