{"id":"https://openalex.org/W4389381430","doi":"https://doi.org/10.1007/s10817-023-09686-y","title":"Formally-Verified Round-Off Error Analysis of Runge\u2013Kutta Methods","display_name":"Formally-Verified Round-Off Error Analysis of Runge\u2013Kutta Methods","publication_year":2023,"publication_date":"2023-12-06","ids":{"openalex":"https://openalex.org/W4389381430","doi":"https://doi.org/10.1007/s10817-023-09686-y"},"language":"en","primary_location":{"id":"doi:10.1007/s10817-023-09686-y","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1007/s10817-023-09686-y","pdf_url":null,"source":{"id":"https://openalex.org/S99781599","display_name":"Journal of Automated Reasoning","issn_l":"0168-7433","issn":["0168-7433","1573-0670"],"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 Automated Reasoning","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/A5059583982","display_name":"Florian Faissole","orcid":"https://orcid.org/0000-0001-5792-0658"},"institutions":[{"id":"https://openalex.org/I4210089619","display_name":"Mitsubishi Electric (France)","ror":"https://ror.org/0075b7k59","country_code":"FR","type":"company","lineage":["https://openalex.org/I1306287861","https://openalex.org/I4210089619","https://openalex.org/I4210133125"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Florian Faissole","raw_affiliation_strings":["Mitsubishi Electric R &D Centre Europe, 1 all\u00e9e de Beaulieu, 35700, Rennes, France","Mitsubishi Electric R &D Centre Europe, Rennes, France"],"raw_orcid":"https://orcid.org/0000-0001-5792-0658","affiliations":[{"raw_affiliation_string":"Mitsubishi Electric R &D Centre Europe, 1 all\u00e9e de Beaulieu, 35700, Rennes, France","institution_ids":["https://openalex.org/I4210089619"]},{"raw_affiliation_string":"Mitsubishi Electric R &D Centre Europe, Rennes, France","institution_ids":["https://openalex.org/I4210089619"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5059583982"],"corresponding_institution_ids":["https://openalex.org/I4210089619"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":0.4277,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.65808178,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"68","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9998999834060669,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9900000095367432,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9824000000953674,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/rounding","display_name":"Rounding","score":0.8432387113571167},{"id":"https://openalex.org/keywords/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.7574095726013184},{"id":"https://openalex.org/keywords/round-off-error","display_name":"Round-off error","score":0.7309173345565796},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.562172532081604},{"id":"https://openalex.org/keywords/machine-epsilon","display_name":"Machine epsilon","score":0.5512519478797913},{"id":"https://openalex.org/keywords/arithmetic-underflow","display_name":"Arithmetic underflow","score":0.5069801807403564},{"id":"https://openalex.org/keywords/floating-point","display_name":"Floating point","score":0.4776826500892639},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46422430872917175},{"id":"https://openalex.org/keywords/linear-multistep-method","display_name":"Linear multistep method","score":0.45125943422317505},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.450484037399292},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.4475378692150116},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.43929535150527954},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4378814697265625},{"id":"https://openalex.org/keywords/numerical-methods-for-ordinary-differential-equations","display_name":"Numerical methods for ordinary differential equations","score":0.43344181776046753},{"id":"https://openalex.org/keywords/euler-method","display_name":"Euler method","score":0.4294532239437103},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.39273571968078613},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.36161571741104126},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35811474919319153},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.34574633836746216},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.17645809054374695},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10701870918273926}],"concepts":[{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.8432387113571167},{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.7574095726013184},{"id":"https://openalex.org/C61005703","wikidata":"https://www.wikidata.org/wiki/Q2145211","display_name":"Round-off error","level":2,"score":0.7309173345565796},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.562172532081604},{"id":"https://openalex.org/C203739276","wikidata":"https://www.wikidata.org/wiki/Q1780355","display_name":"Machine epsilon","level":2,"score":0.5512519478797913},{"id":"https://openalex.org/C3265923","wikidata":"https://www.wikidata.org/wiki/Q669129","display_name":"Arithmetic underflow","level":2,"score":0.5069801807403564},{"id":"https://openalex.org/C84211073","wikidata":"https://www.wikidata.org/wiki/Q117879","display_name":"Floating point","level":2,"score":0.4776826500892639},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46422430872917175},{"id":"https://openalex.org/C65889100","wikidata":"https://www.wikidata.org/wiki/Q1462003","display_name":"Linear multistep method","level":5,"score":0.45125943422317505},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.450484037399292},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.4475378692150116},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.43929535150527954},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4378814697265625},{"id":"https://openalex.org/C1164432","wikidata":"https://www.wikidata.org/wiki/Q541182","display_name":"Numerical methods for ordinary differential equations","level":5,"score":0.43344181776046753},{"id":"https://openalex.org/C75380026","wikidata":"https://www.wikidata.org/wiki/Q868454","display_name":"Euler method","level":3,"score":0.4294532239437103},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.39273571968078613},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.36161571741104126},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35811474919319153},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.34574633836746216},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.17645809054374695},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10701870918273926},{"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10817-023-09686-y","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1007/s10817-023-09686-y","pdf_url":null,"source":{"id":"https://openalex.org/S99781599","display_name":"Journal of Automated Reasoning","issn_l":"0168-7433","issn":["0168-7433","1573-0670"],"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 Automated Reasoning","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5293329413","display_name":"Fast Reliable Approximation","funder_award_id":"ANR-14-CE25-0018","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":61,"referenced_works":["https://openalex.org/W56092462","https://openalex.org/W306903215","https://openalex.org/W605824955","https://openalex.org/W970850559","https://openalex.org/W1482491673","https://openalex.org/W1483804921","https://openalex.org/W1500006811","https://openalex.org/W1542112699","https://openalex.org/W1615140576","https://openalex.org/W1912797367","https://openalex.org/W1964474305","https://openalex.org/W1968813561","https://openalex.org/W1969213662","https://openalex.org/W1975906542","https://openalex.org/W1980426569","https://openalex.org/W1995320858","https://openalex.org/W1998583908","https://openalex.org/W1999470254","https://openalex.org/W2020804487","https://openalex.org/W2028342439","https://openalex.org/W2042386348","https://openalex.org/W2042388195","https://openalex.org/W2056352173","https://openalex.org/W2121020818","https://openalex.org/W2138211565","https://openalex.org/W2139410404","https://openalex.org/W2147177731","https://openalex.org/W2149412820","https://openalex.org/W2150118230","https://openalex.org/W2151313505","https://openalex.org/W2167447262","https://openalex.org/W2169004268","https://openalex.org/W2213989452","https://openalex.org/W2269854487","https://openalex.org/W2292537122","https://openalex.org/W2304289376","https://openalex.org/W2315651828","https://openalex.org/W2483648716","https://openalex.org/W2498647973","https://openalex.org/W2546463436","https://openalex.org/W2561211292","https://openalex.org/W2736053689","https://openalex.org/W2786716769","https://openalex.org/W2790158899","https://openalex.org/W2791728102","https://openalex.org/W2792892743","https://openalex.org/W2804372380","https://openalex.org/W2887787479","https://openalex.org/W2903340267","https://openalex.org/W3103675537","https://openalex.org/W3138238758","https://openalex.org/W3138624857","https://openalex.org/W3164690045","https://openalex.org/W4230575278","https://openalex.org/W4236023018","https://openalex.org/W4242300732","https://openalex.org/W4249473960","https://openalex.org/W4293515545","https://openalex.org/W6601145284","https://openalex.org/W6629628904","https://openalex.org/W6676917639"],"related_works":["https://openalex.org/W1995404603","https://openalex.org/W1926143101","https://openalex.org/W3091448100","https://openalex.org/W2048226115","https://openalex.org/W2188177662","https://openalex.org/W2358336335","https://openalex.org/W3123524152","https://openalex.org/W4230605333","https://openalex.org/W4229586813","https://openalex.org/W2060587726"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
