{"id":"https://openalex.org/W2068343263","doi":"https://doi.org/10.1016/s1571-0661(04)80774-6","title":"On the construction of a new generalization of Runge\u2013Kutta methods","display_name":"On the construction of a new generalization of Runge\u2013Kutta methods","publication_year":2003,"publication_date":"2003-10-01","ids":{"openalex":"https://openalex.org/W2068343263","doi":"https://doi.org/10.1016/s1571-0661(04)80774-6","mag":"2068343263"},"language":"en","primary_location":{"id":"doi:10.1016/s1571-0661(04)80774-6","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(04)80774-6","pdf_url":null,"source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.1016/s1571-0661(04)80774-6","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071931857","display_name":"Mark Sofroniou","orcid":null},"institutions":[{"id":"https://openalex.org/I65760639","display_name":"Wolfram Research (United States)","ror":"https://ror.org/03k118f17","country_code":"US","type":"company","lineage":["https://openalex.org/I65760639"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Mark Sofroniou","raw_affiliation_strings":["Department of Research and Development, Wolfram Research Inc., Champaign, Illinois, USA"],"affiliations":[{"raw_affiliation_string":"Department of Research and Development, Wolfram Research Inc., Champaign, Illinois, USA","institution_ids":["https://openalex.org/I65760639"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045302264","display_name":"Giulia Spaletta","orcid":"https://orcid.org/0000-0002-6871-0864"},"institutions":[{"id":"https://openalex.org/I9360294","display_name":"University of Bologna","ror":"https://ror.org/01111rn36","country_code":"IT","type":"education","lineage":["https://openalex.org/I9360294"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Giulia Spaletta","raw_affiliation_strings":["Department of Mathematics, Bologna University, Piazza Porta S. Donato 5, 40127 Bologna, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Bologna University, Piazza Porta S. Donato 5, 40127 Bologna, Italy","institution_ids":["https://openalex.org/I9360294"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5045302264","https://openalex.org/A5071931857"],"corresponding_institution_ids":["https://openalex.org/I65760639","https://openalex.org/I9360294"],"apc_list":null,"apc_paid":null,"fwci":0.8649,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.74404237,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"74","issue":null,"first_page":"189","last_page":"206"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9952999949455261,"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":0.9901000261306763,"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":0.9371907114982605},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6624600291252136},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5442841053009033},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5300756692886353},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.502220630645752},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.4915100038051605},{"id":"https://openalex.org/keywords/taylor-series","display_name":"Taylor series","score":0.4816259741783142},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4679735004901886},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.44577810168266296},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.4424899220466614},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.4405987858772278},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.415409654378891},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3576884865760803},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.35406702756881714},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22813060879707336},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.12501224875450134}],"concepts":[{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.9371907114982605},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6624600291252136},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5442841053009033},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5300756692886353},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.502220630645752},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.4915100038051605},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.4816259741783142},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4679735004901886},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.44577810168266296},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4424899220466614},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.4405987858772278},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.415409654378891},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3576884865760803},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.35406702756881714},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22813060879707336},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.12501224875450134},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1016/s1571-0661(04)80774-6","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(04)80774-6","pdf_url":null,"source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:cris.unibo.it:11585/880465","is_oa":false,"landing_page_url":"http://hdl.handle.net/11585/880465","pdf_url":null,"source":{"id":"https://openalex.org/S4306402579","display_name":"Archivio istituzionale della ricerca (Alma Mater Studiorum Universit\u00e0 di Bologna)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210117483","host_organization_name":"Istituto di Ematologia di Bologna","host_organization_lineage":["https://openalex.org/I4210117483"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:cris.unibo.it:11585/881296","is_oa":false,"landing_page_url":"https://hdl.handle.net/11585/881296","pdf_url":null,"source":{"id":"https://openalex.org/S4306402579","display_name":"Archivio istituzionale della ricerca (Alma Mater Studiorum Universit\u00e0 di Bologna)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210117483","host_organization_name":"Istituto di Ematologia di Bologna","host_organization_lineage":["https://openalex.org/I4210117483"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1016/s1571-0661(04)80774-6","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(04)80774-6","pdf_url":null,"source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W175137405","https://openalex.org/W1509923322","https://openalex.org/W1524590822","https://openalex.org/W1560244967","https://openalex.org/W1981733036","https://openalex.org/W1995997000","https://openalex.org/W1997270188","https://openalex.org/W2042388195","https://openalex.org/W2063269749","https://openalex.org/W2068343263","https://openalex.org/W2073477729","https://openalex.org/W2080544145","https://openalex.org/W2084367325","https://openalex.org/W2095817904","https://openalex.org/W2122336811","https://openalex.org/W2799004609","https://openalex.org/W2947056241","https://openalex.org/W2981569720","https://openalex.org/W3016843226","https://openalex.org/W4254566809","https://openalex.org/W6671481900"],"related_works":["https://openalex.org/W4206768127","https://openalex.org/W4213270568","https://openalex.org/W4244999877","https://openalex.org/W4301315183","https://openalex.org/W2083551655","https://openalex.org/W2157764110","https://openalex.org/W2121498459","https://openalex.org/W2811272663","https://openalex.org/W3008473368","https://openalex.org/W2047656848"],"abstract_inverted_index":{"We":[0,49],"give":[1,67],"an":[2],"overview":[3],"of":[4,7,14,26],"the":[5,12,58],"construction":[6],"algebraic":[8],"conditions":[9,53],"for":[10,22,57],"determining":[11],"order":[13,52],"Runge-Kutta":[15,35,41,47],"methods":[16],"and":[17,63,66],"describe":[18],"a":[19,39,71],"novel":[20],"extension":[21],"numerically":[23],"solving":[24],"systems":[25],"differential":[27],"equations.":[28],"The":[29],"new":[30,59],"schemes,":[31],"called":[32],"Elementary":[33],"Differential":[34],"methods,":[36,42,45],"include":[37],"as":[38],"subset":[40],"Taylor":[43],"series":[44],"Multiderivative":[46],"methods.":[48],"outline":[50],"how":[51],"have":[54],"been":[55],"constructed":[56],"schemes":[60],"using":[61],"B-series":[62],"their":[64],"composition":[65],"details":[68],"relating":[69],"to":[70],"Mathematica":[72],"implementation.":[73]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2016-06-24T00:00:00"}
