{"id":"https://openalex.org/W1584922436","doi":"https://doi.org/10.1007/11758501_22","title":"Local Linearization-Runge Kutta (LLRK) Methods for Solving Ordinary Differential Equations","display_name":"Local Linearization-Runge Kutta (LLRK) Methods for Solving Ordinary Differential Equations","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W1584922436","doi":"https://doi.org/10.1007/11758501_22","mag":"1584922436"},"language":"en","primary_location":{"id":"doi:10.1007/11758501_22","is_oa":false,"landing_page_url":"https://doi.org/10.1007/11758501_22","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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":null,"display_name":"H. De la Cruz","orcid":null},"institutions":[{"id":"https://openalex.org/I4210102241","display_name":"University of Information Science","ror":"https://ror.org/022camr20","country_code":"CU","type":"education","lineage":["https://openalex.org/I4210102241"]},{"id":"https://openalex.org/I4210147029","display_name":"University of Granma","ror":"https://ror.org/0488pxx86","country_code":"CU","type":"education","lineage":["https://openalex.org/I4210147029"]}],"countries":["CU"],"is_corresponding":false,"raw_author_name":"H. De la Cruz","raw_affiliation_strings":["Universidad de Granma, Bayamo, MN, Cuba","Universidad de las Ciencias Inform\u00e1ticas, La Habana, Cuba"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universidad de Granma, Bayamo, MN, Cuba","institution_ids":["https://openalex.org/I4210147029"]},{"raw_affiliation_string":"Universidad de las Ciencias Inform\u00e1ticas, La Habana, Cuba","institution_ids":["https://openalex.org/I4210102241"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113652079","display_name":"R. Biscay","orcid":null},"institutions":[{"id":"https://openalex.org/I4210119680","display_name":"Instituto de Cibern\u00e9tica Matem\u00e1tica y F\u00edsica","ror":"https://ror.org/02n3qcb27","country_code":"CU","type":"facility","lineage":["https://openalex.org/I4210119680"]}],"countries":["CU"],"is_corresponding":false,"raw_author_name":"R. J. Biscay","raw_affiliation_strings":["Instituto de Cibern\u00e9tica, Matem\u00e1tica y F\u00edsica, La Habana, Cuba"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Cibern\u00e9tica, Matem\u00e1tica y F\u00edsica, La Habana, Cuba","institution_ids":["https://openalex.org/I4210119680"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017703525","display_name":"F\u00e9lix Carbonell","orcid":"https://orcid.org/0000-0002-1450-0423"},"institutions":[{"id":"https://openalex.org/I4210119680","display_name":"Instituto de Cibern\u00e9tica Matem\u00e1tica y F\u00edsica","ror":"https://ror.org/02n3qcb27","country_code":"CU","type":"facility","lineage":["https://openalex.org/I4210119680"]}],"countries":["CU"],"is_corresponding":false,"raw_author_name":"F. Carbonell","raw_affiliation_strings":["Instituto de Cibern\u00e9tica, Matem\u00e1tica y F\u00edsica, La Habana, Cuba"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Cibern\u00e9tica, Matem\u00e1tica y F\u00edsica, La Habana, Cuba","institution_ids":["https://openalex.org/I4210119680"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073285867","display_name":"Juan Carlos Jim\u00e9nez","orcid":"https://orcid.org/0000-0001-6014-0505"},"institutions":[{"id":"https://openalex.org/I4210119680","display_name":"Instituto de Cibern\u00e9tica Matem\u00e1tica y F\u00edsica","ror":"https://ror.org/02n3qcb27","country_code":"CU","type":"facility","lineage":["https://openalex.org/I4210119680"]}],"countries":["CU"],"is_corresponding":false,"raw_author_name":"J. C. Jimenez","raw_affiliation_strings":["Instituto de Cibern\u00e9tica, Matem\u00e1tica y F\u00edsica, La Habana, Cuba"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Cibern\u00e9tica, Matem\u00e1tica y F\u00edsica, La Habana, Cuba","institution_ids":["https://openalex.org/I4210119680"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029948282","display_name":"Tohru Ozaki","orcid":null},"institutions":[{"id":"https://openalex.org/I4210134673","display_name":"The Institute of Statistical Mathematics","ror":"https://ror.org/03jcejr58","country_code":"JP","type":"facility","lineage":["https://openalex.org/I1319490839","https://openalex.org/I4210134673","https://openalex.org/I4210158934"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"T. Ozaki","raw_affiliation_strings":["Institute of Statistical Mathematics, Tokyo, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Statistical Mathematics, Tokyo, Japan","institution_ids":["https://openalex.org/I4210134673"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":3.2544,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.94196429,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"132","last_page":"139"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9872000217437744,"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":0.9846000075340271,"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":0.8165502548217773},{"id":"https://openalex.org/keywords/integrator","display_name":"Integrator","score":0.7664729356765747},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.7513065338134766},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.7079466581344604},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6151984930038452},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6043410301208496},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.562084972858429},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5080440044403076},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5006520748138428},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47457364201545715},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.45981156826019287},{"id":"https://openalex.org/keywords/numerical-methods-for-ordinary-differential-equations","display_name":"Numerical methods for ordinary differential equations","score":0.4180668592453003},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.37962812185287476},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.24459269642829895},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23363667726516724},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1828761100769043},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05349564552307129}],"concepts":[{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.8165502548217773},{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.7664729356765747},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.7513065338134766},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.7079466581344604},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6151984930038452},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6043410301208496},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.562084972858429},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5080440044403076},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5006520748138428},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47457364201545715},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.45981156826019287},{"id":"https://openalex.org/C1164432","wikidata":"https://www.wikidata.org/wiki/Q541182","display_name":"Numerical methods for ordinary differential equations","level":5,"score":0.4180668592453003},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.37962812185287476},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.24459269642829895},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23363667726516724},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1828761100769043},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05349564552307129},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"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/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/11758501_22","is_oa":false,"landing_page_url":"https://doi.org/10.1007/11758501_22","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1509923322","https://openalex.org/W1600945564","https://openalex.org/W1964024787","https://openalex.org/W1984840946","https://openalex.org/W1995014455","https://openalex.org/W1995504856","https://openalex.org/W2008007187","https://openalex.org/W2010652522","https://openalex.org/W2015331666","https://openalex.org/W2017996934","https://openalex.org/W2054420328","https://openalex.org/W2063825233","https://openalex.org/W2068806687","https://openalex.org/W2071007053","https://openalex.org/W2106565812","https://openalex.org/W2120516507","https://openalex.org/W2310212366","https://openalex.org/W2981569720","https://openalex.org/W4245463005","https://openalex.org/W4249113602"],"related_works":["https://openalex.org/W2243194968","https://openalex.org/W47811045","https://openalex.org/W2278428637","https://openalex.org/W2098889120","https://openalex.org/W2949519336","https://openalex.org/W2030407843","https://openalex.org/W2441932228","https://openalex.org/W2021809153","https://openalex.org/W4240815253","https://openalex.org/W2041014535"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}