{"id":"https://openalex.org/W3034558347","doi":"https://doi.org/10.1007/s40314-020-01214-7","title":"Hybrid Runge\u2013Kutta methods for ordinary differential equations","display_name":"Hybrid Runge\u2013Kutta methods for ordinary differential equations","publication_year":2020,"publication_date":"2020-06-09","ids":{"openalex":"https://openalex.org/W3034558347","doi":"https://doi.org/10.1007/s40314-020-01214-7","mag":"3034558347"},"language":"en","primary_location":{"id":"doi:10.1007/s40314-020-01214-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-020-01214-7","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"1807-0302","issn":["1807-0302","2238-3603"],"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":"Computational and Applied 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/A5061231533","display_name":"Zhongli Liu","orcid":"https://orcid.org/0000-0002-3234-310X"},"institutions":[{"id":"https://openalex.org/I905225518","display_name":"Shanghai University of International Business and Economics","ror":"https://ror.org/031t68441","country_code":"CN","type":"education","lineage":["https://openalex.org/I905225518"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhongli Liu","raw_affiliation_strings":["School of Statistics and Information, Shanghai University of International Business and Economics, 1900 Wenxiang Road, Shanghai, 201620, China"],"affiliations":[{"raw_affiliation_string":"School of Statistics and Information, Shanghai University of International Business and Economics, 1900 Wenxiang Road, Shanghai, 201620, China","institution_ids":["https://openalex.org/I905225518"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083511583","display_name":"Jintao Hu","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"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jintao Hu","raw_affiliation_strings":["Department of Mathematics, Shanghai Normal University, Shanghai, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai Normal University, Shanghai, China","institution_ids":["https://openalex.org/I21945476"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100828217","display_name":"Hongjiong Tian","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"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hongjiong Tian","raw_affiliation_strings":["Department of Mathematics, Shanghai Normal University, Shanghai, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai Normal University, Shanghai, China","institution_ids":["https://openalex.org/I21945476"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5061231533","https://openalex.org/A5100828217"],"corresponding_institution_ids":["https://openalex.org/I21945476","https://openalex.org/I905225518"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.10507922,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"39","issue":"3","first_page":null,"last_page":null},"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"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":0.9972000122070312,"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":0.9576531648635864},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6898806095123291},{"id":"https://openalex.org/keywords/numerical-methods-for-ordinary-differential-equations","display_name":"Numerical methods for ordinary differential equations","score":0.6622008681297302},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6399081349372864},{"id":"https://openalex.org/keywords/l-stability","display_name":"L-stability","score":0.6326498985290527},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5306039452552795},{"id":"https://openalex.org/keywords/explicit-and-implicit-methods","display_name":"Explicit and implicit methods","score":0.514025092124939},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.5101264119148254},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.46050378680229187},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4371374845504761},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3775283694267273},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.30865341424942017},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23442068696022034}],"concepts":[{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.9576531648635864},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6898806095123291},{"id":"https://openalex.org/C1164432","wikidata":"https://www.wikidata.org/wiki/Q541182","display_name":"Numerical methods for ordinary differential equations","level":5,"score":0.6622008681297302},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6399081349372864},{"id":"https://openalex.org/C165242687","wikidata":"https://www.wikidata.org/wiki/Q277932","display_name":"L-stability","level":5,"score":0.6326498985290527},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5306039452552795},{"id":"https://openalex.org/C149393637","wikidata":"https://www.wikidata.org/wiki/Q5421265","display_name":"Explicit and implicit methods","level":5,"score":0.514025092124939},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.5101264119148254},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.46050378680229187},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4371374845504761},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3775283694267273},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.30865341424942017},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23442068696022034},{"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s40314-020-01214-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-020-01214-7","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"1807-0302","issn":["1807-0302","2238-3603"],"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":"Computational and Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1942198446","display_name":null,"funder_award_id":"11671266","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W9124626","https://openalex.org/W1509923322","https://openalex.org/W1974130402","https://openalex.org/W1982034332","https://openalex.org/W1989955731","https://openalex.org/W1995504856","https://openalex.org/W2042388195","https://openalex.org/W2078427129","https://openalex.org/W2144375544","https://openalex.org/W2151807147","https://openalex.org/W2319973481","https://openalex.org/W2981569720","https://openalex.org/W3023305542"],"related_works":["https://openalex.org/W2136451125","https://openalex.org/W181177096","https://openalex.org/W2088005785","https://openalex.org/W2378531610","https://openalex.org/W2278428637","https://openalex.org/W1982032924","https://openalex.org/W2956395387","https://openalex.org/W2185332433","https://openalex.org/W1579385565","https://openalex.org/W797453289"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
