{"id":"https://openalex.org/W4415250757","doi":"https://doi.org/10.1109/hpec67600.2025.11196706","title":"A Fully Adaptive Radau Method for the Efficient Solution of Stiff Ordinary Differential Equations at Low Tolerances","display_name":"A Fully Adaptive Radau Method for the Efficient Solution of Stiff Ordinary Differential Equations at Low Tolerances","publication_year":2025,"publication_date":"2025-09-15","ids":{"openalex":"https://openalex.org/W4415250757","doi":"https://doi.org/10.1109/hpec67600.2025.11196706"},"language":"en","primary_location":{"id":"doi:10.1109/hpec67600.2025.11196706","is_oa":false,"landing_page_url":"https://doi.org/10.1109/hpec67600.2025.11196706","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2025 IEEE High Performance Extreme Computing Conference (HPEC)","raw_type":"proceedings-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/A5115561115","display_name":"Shreyas Ekanathan","orcid":null},"institutions":[{"id":"https://openalex.org/I4210143528","display_name":"Lexington City Schools","ror":"https://ror.org/043f52r95","country_code":"US","type":"education","lineage":["https://openalex.org/I4210143528"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Shreyas Ekanathan","raw_affiliation_strings":["Lexington High School,Lexington,Massachusetts,USA"],"affiliations":[{"raw_affiliation_string":"Lexington High School,Lexington,Massachusetts,USA","institution_ids":["https://openalex.org/I4210143528"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Oscar Smith","orcid":null},"institutions":[{"id":"https://openalex.org/I4210096386","display_name":"Bridge University","ror":"https://ror.org/00cbm0437","country_code":"SS","type":"education","lineage":["https://openalex.org/I4210096386"]}],"countries":["SS"],"is_corresponding":false,"raw_author_name":"Oscar Smith","raw_affiliation_strings":["JuliaHub,Cambridge,Massachusetts,USA"],"affiliations":[{"raw_affiliation_string":"JuliaHub,Cambridge,Massachusetts,USA","institution_ids":["https://openalex.org/I4210096386"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043195923","display_name":"Christopher Rackauckas","orcid":"https://orcid.org/0000-0001-5850-0663"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Christopher Rackauckas","raw_affiliation_strings":["Pumas AI Inc.,JuliaHub Massachusetts Institute of Technology,Cambridge,Massachusetts,USA"],"affiliations":[{"raw_affiliation_string":"Pumas AI Inc.,JuliaHub Massachusetts Institute of Technology,Cambridge,Massachusetts,USA","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5115561115"],"corresponding_institution_ids":["https://openalex.org/I4210143528"],"apc_list":null,"apc_paid":null,"fwci":2.4313,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.9017915,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"9"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9846000075340271,"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":0.9846000075340271,"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":0.9811999797821045,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9598000049591064,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.6733999848365784},{"id":"https://openalex.org/keywords/fortran","display_name":"Fortran","score":0.6682999730110168},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6561999917030334},{"id":"https://openalex.org/keywords/integrator","display_name":"Integrator","score":0.6209999918937683},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.602400004863739},{"id":"https://openalex.org/keywords/backward-differentiation-formula","display_name":"Backward differentiation formula","score":0.569100022315979},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.48910000920295715},{"id":"https://openalex.org/keywords/stiff-equation","display_name":"Stiff equation","score":0.48100000619888306},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4323999881744385},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.40860000252723694}],"concepts":[{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.6733999848365784},{"id":"https://openalex.org/C2778241615","wikidata":"https://www.wikidata.org/wiki/Q83303","display_name":"Fortran","level":2,"score":0.6682999730110168},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6561999917030334},{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.6209999918937683},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.602400004863739},{"id":"https://openalex.org/C152522140","wikidata":"https://www.wikidata.org/wiki/Q795746","display_name":"Backward differentiation formula","level":5,"score":0.569100022315979},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5590999722480774},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.48910000920295715},{"id":"https://openalex.org/C43012357","wikidata":"https://www.wikidata.org/wiki/Q29744","display_name":"Stiff equation","level":3,"score":0.48100000619888306},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4666000008583069},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4323999881744385},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41839998960494995},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.40860000252723694},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.39730000495910645},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.39660000801086426},{"id":"https://openalex.org/C122700484","wikidata":"https://www.wikidata.org/wiki/Q16148845","display_name":"Exponential integrator","level":5,"score":0.3659999966621399},{"id":"https://openalex.org/C39177556","wikidata":"https://www.wikidata.org/wiki/Q7100567","display_name":"Order of accuracy","level":4,"score":0.3605000078678131},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3296999931335449},{"id":"https://openalex.org/C149393637","wikidata":"https://www.wikidata.org/wiki/Q5421265","display_name":"Explicit and implicit methods","level":5,"score":0.3294999897480011},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.320499986410141},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2976999878883362},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.2976999878883362},{"id":"https://openalex.org/C48077252","wikidata":"https://www.wikidata.org/wiki/Q4680766","display_name":"Adaptive stepsize","level":3,"score":0.29649999737739563},{"id":"https://openalex.org/C165242687","wikidata":"https://www.wikidata.org/wiki/Q277932","display_name":"L-stability","level":5,"score":0.2904999852180481},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.2896000146865845},{"id":"https://openalex.org/C139807058","wikidata":"https://www.wikidata.org/wiki/Q352374","display_name":"Adaptation (eye)","level":2,"score":0.28780001401901245},{"id":"https://openalex.org/C147504518","wikidata":"https://www.wikidata.org/wiki/Q2146125","display_name":"Delay differential equation","level":3,"score":0.2791999876499176},{"id":"https://openalex.org/C113364801","wikidata":"https://www.wikidata.org/wiki/Q26674","display_name":"High fidelity","level":2,"score":0.27730000019073486},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.27320000529289246},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.26440000534057617},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.26409998536109924},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.2612000107765198},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2563999891281128},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.25200000405311584},{"id":"https://openalex.org/C131053463","wikidata":"https://www.wikidata.org/wiki/Q4680751","display_name":"Adaptive mesh refinement","level":2,"score":0.25130000710487366}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/hpec67600.2025.11196706","is_oa":false,"landing_page_url":"https://doi.org/10.1109/hpec67600.2025.11196706","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2025 IEEE High Performance Extreme Computing Conference (HPEC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W42591571","https://openalex.org/W1995504856","https://openalex.org/W2029290244","https://openalex.org/W2030276156","https://openalex.org/W2030757524","https://openalex.org/W2056775673","https://openalex.org/W2067444308","https://openalex.org/W2070415065","https://openalex.org/W2076955670","https://openalex.org/W2081518023","https://openalex.org/W2098168282","https://openalex.org/W2117453669","https://openalex.org/W2120575449","https://openalex.org/W2166751342","https://openalex.org/W2589540362","https://openalex.org/W2619381903","https://openalex.org/W2963232822","https://openalex.org/W3107880782","https://openalex.org/W4255754126","https://openalex.org/W4304806418","https://openalex.org/W4308090253","https://openalex.org/W4362673400","https://openalex.org/W4366085193","https://openalex.org/W4392766660"],"related_works":[],"abstract_inverted_index":{"Radau":[0,7,85,94],"IIA":[1,95],"methods,":[2],"specifically":[3],"the":[4,20,31,53,65,90,93,102,120,134],"adaptive":[5],"order":[6,50,100,121],"method":[8,86,191],"in":[9,42,58,194],"Fortran":[10,136],"due":[11],"to":[12,16,36,67,98,104,114,119],"Hairer,":[13],"are":[14],"known":[15],"be":[17,68],"state-of-the-art":[18,165],"for":[19,72,92,160,179,198],"high-accuracy":[21],"solution":[22],"of":[23,40,52,148],"highly":[24],"stiff":[25,149,161,180,202],"ordinary":[26],"differential":[27],"equations":[28],"(ODEs).":[29],"However,":[30],"traditional":[32],"implementation":[33,110,141],"was":[34],"specialized":[35],"a":[37,130,146,172],"specific":[38],"range":[39,147],"tolerance,":[41],"particular":[43],"only":[44,56],"supporting":[45],"5th,":[46],"9th,":[47],"and":[48,55,124,163],"13th":[49],"versions":[51],"tableau":[54,97],"derived":[57],"double":[59],"precision":[60],"floating":[61],"point,":[62],"thus":[63],"limiting":[64],"ability":[66],"truly":[69],"general":[70],"purpose":[71],"high":[73],"fidelity":[74],"scenarios.":[75],"To":[76],"alleviate":[77],"these":[78],"constraints,":[79],"we":[80,138],"implement":[81],"an":[82],"adaptive-time":[83],"adaptive-order":[84],"which":[87],"can":[88],"derive":[89],"coefficients":[91],"embedded":[96],"any":[99,105],"on":[101,167,201],"fly":[103],"precision.":[106],"Additionally,":[107],"our":[108,140,153],"Julia-based":[109],"includes":[111],"many":[112],"modernizations":[113],"improve":[115],"performance,":[116],"including":[117],"improvements":[118],"adaptation":[122],"scheme":[123],"improved":[125],"linear":[126],"algebra":[127],"integrations.":[128],"In":[129],"head-to-head":[131],"benchmark":[132,152],"against":[133,155],"classic":[135],"implementation,":[137],"demonstrate":[139],"is":[142,186,192],"approximately":[143],"2x":[144],"across":[145],"ODEs.":[150,203],"We":[151],"algorithm":[154],"several":[156,168],"well-reputed":[157],"numerical":[158,177],"integrators":[159,178],"ODEs":[162,181],"find":[164],"performance":[166],"test":[169],"problems,":[170],"with":[171],"1.5x":[173],"speed-up":[174],"over":[175],"common":[176],"when":[182],"low":[183],"error":[184],"tolerance":[185],"required.":[187],"The":[188],"newly":[189],"implemented":[190],"distributed":[193],"open":[195],"source":[196],"software":[197],"free":[199],"usage":[200]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-04-17T18:11:37.981687","created_date":"2025-10-16T00:00:00"}
