{"id":"https://openalex.org/W2063457282","doi":"https://doi.org/10.1007/s10915-011-9538-7","title":"Legendre-Gauss-Radau Collocation Method for Solving Initial Value Problems of First Order Ordinary Differential Equations","display_name":"Legendre-Gauss-Radau Collocation Method for Solving Initial Value Problems of First Order Ordinary Differential Equations","publication_year":2011,"publication_date":"2011-09-21","ids":{"openalex":"https://openalex.org/W2063457282","doi":"https://doi.org/10.1007/s10915-011-9538-7","mag":"2063457282"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-011-9538-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-011-9538-7","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","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/A5100369600","display_name":"Zhongqing Wang","orcid":"https://orcid.org/0000-0002-3281-5322"},"institutions":[{"id":"https://openalex.org/I21945476","display_name":"Shanghai Normal University","ror":"https://ror.org/01cxqmw89","country_code":"CN","type":"education","lineage":["https://openalex.org/I21945476"]},{"id":"https://openalex.org/I4210160248","display_name":"Shanghai Universities E-Institute for Chemical Biology","ror":"https://ror.org/03h7eyw97","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210160248"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhong-qing Wang","raw_affiliation_strings":["Department of Mathematics, Shanghai Normal University, Shanghai, 200234, P.R. China","Scientific Computing Key Laboratory of Shanghai Universities, Division of Computational Science of E-institute of Shanghai Universities, Shanghai, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai Normal University, Shanghai, 200234, P.R. China","institution_ids":["https://openalex.org/I21945476"]},{"raw_affiliation_string":"Scientific Computing Key Laboratory of Shanghai Universities, Division of Computational Science of E-institute of Shanghai Universities, Shanghai, P.R. China","institution_ids":["https://openalex.org/I4210160248"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112630309","display_name":"Ben\u2010yu Guo","orcid":null},"institutions":[{"id":"https://openalex.org/I21945476","display_name":"Shanghai Normal University","ror":"https://ror.org/01cxqmw89","country_code":"CN","type":"education","lineage":["https://openalex.org/I21945476"]},{"id":"https://openalex.org/I4210160248","display_name":"Shanghai Universities E-Institute for Chemical Biology","ror":"https://ror.org/03h7eyw97","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210160248"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ben-yu Guo","raw_affiliation_strings":["Department of Mathematics, Shanghai Normal University, Shanghai, 200234, P.R. China","Scientific Computing Key Laboratory of Shanghai Universities, Division of Computational Science of E-institute of Shanghai Universities, Shanghai, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai Normal University, Shanghai, 200234, P.R. China","institution_ids":["https://openalex.org/I21945476"]},{"raw_affiliation_string":"Scientific Computing Key Laboratory of Shanghai Universities, Division of Computational Science of E-institute of Shanghai Universities, Shanghai, P.R. China","institution_ids":["https://openalex.org/I4210160248"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100369600"],"corresponding_institution_ids":["https://openalex.org/I21945476","https://openalex.org/I4210160248"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":7.3425,"has_fulltext":false,"cited_by_count":63,"citation_normalized_percentile":{"value":0.97268817,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"52","issue":"1","first_page":"226","last_page":"255"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":1.0,"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":1.0,"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":0.9984999895095825,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9958999752998352,"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":0.8749535083770752},{"id":"https://openalex.org/keywords/legendre-polynomials","display_name":"Legendre polynomials","score":0.7041968703269958},{"id":"https://openalex.org/keywords/gauss","display_name":"Gauss","score":0.6933332681655884},{"id":"https://openalex.org/keywords/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.6389424204826355},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.6089258790016174},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6040148735046387},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.5823632478713989},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5687559247016907},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.550402045249939},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.5371786952018738},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5339891314506531},{"id":"https://openalex.org/keywords/spectral-method","display_name":"Spectral method","score":0.45521989464759827},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4536657929420471},{"id":"https://openalex.org/keywords/orthogonal-collocation","display_name":"Orthogonal collocation","score":0.45023709535598755},{"id":"https://openalex.org/keywords/numerical-methods-for-ordinary-differential-equations","display_name":"Numerical methods for ordinary differential equations","score":0.4265536963939667},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.41975829005241394},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0715450644493103}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8749535083770752},{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.7041968703269958},{"id":"https://openalex.org/C161794534","wikidata":"https://www.wikidata.org/wiki/Q177493","display_name":"Gauss","level":2,"score":0.6933332681655884},{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.6389424204826355},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.6089258790016174},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6040148735046387},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.5823632478713989},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5687559247016907},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.550402045249939},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.5371786952018738},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5339891314506531},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.45521989464759827},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4536657929420471},{"id":"https://openalex.org/C114609681","wikidata":"https://www.wikidata.org/wiki/Q24839227","display_name":"Orthogonal collocation","level":5,"score":0.45023709535598755},{"id":"https://openalex.org/C1164432","wikidata":"https://www.wikidata.org/wiki/Q541182","display_name":"Numerical methods for ordinary differential equations","level":5,"score":0.4265536963939667},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.41975829005241394},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0715450644493103},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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":1,"locations":[{"id":"doi:10.1007/s10915-011-9538-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-011-9538-7","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W9124626","https://openalex.org/W106404678","https://openalex.org/W579985084","https://openalex.org/W587555435","https://openalex.org/W1509923322","https://openalex.org/W1535429593","https://openalex.org/W1544770838","https://openalex.org/W1805381866","https://openalex.org/W1912930600","https://openalex.org/W1978021397","https://openalex.org/W1983306191","https://openalex.org/W1983422789","https://openalex.org/W1989955731","https://openalex.org/W2004759358","https://openalex.org/W2008007187","https://openalex.org/W2013693242","https://openalex.org/W2014229391","https://openalex.org/W2023049662","https://openalex.org/W2026067503","https://openalex.org/W2028522134","https://openalex.org/W2031567600","https://openalex.org/W2042388195","https://openalex.org/W2048389107","https://openalex.org/W2070514286","https://openalex.org/W2083915368","https://openalex.org/W2084367325","https://openalex.org/W2144375544","https://openalex.org/W2314215937","https://openalex.org/W2335697030","https://openalex.org/W2441183164","https://openalex.org/W2499662517","https://openalex.org/W2591664468","https://openalex.org/W2947056241","https://openalex.org/W3021821037","https://openalex.org/W3150423993","https://openalex.org/W3209416867","https://openalex.org/W4247375400","https://openalex.org/W4285719527","https://openalex.org/W4293515545","https://openalex.org/W4300846967"],"related_works":["https://openalex.org/W2384941625","https://openalex.org/W1843663759","https://openalex.org/W1972053220","https://openalex.org/W2040892753","https://openalex.org/W2158514508","https://openalex.org/W2806218632","https://openalex.org/W3033023825","https://openalex.org/W3096143543","https://openalex.org/W2566202876","https://openalex.org/W2132514189"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}