{"id":"https://openalex.org/W3167961521","doi":"https://doi.org/10.1137/21m1439481","title":"Multirate Exponential Rosenbrock Methods","display_name":"Multirate Exponential Rosenbrock Methods","publication_year":2022,"publication_date":"2022-10-01","ids":{"openalex":"https://openalex.org/W3167961521","doi":"https://doi.org/10.1137/21m1439481","mag":"3167961521"},"language":"en","primary_location":{"id":"doi:10.1137/21m1439481","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1439481","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2106.05385","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069156178","display_name":"V\u0169 Th\u00e1i Lu\u00e2n","orcid":"https://orcid.org/0000-0003-0319-654X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Vu Thai Luan","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-0319-654X","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045470841","display_name":"Rujeko Chinomona","orcid":"https://orcid.org/0000-0002-5267-8433"},"institutions":[{"id":"https://openalex.org/I178169726","display_name":"Southern Methodist University","ror":"https://ror.org/042tdr378","country_code":"US","type":"education","lineage":["https://openalex.org/I178169726"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rujeko Chinomona","raw_affiliation_strings":["Department of Mathematics, Southern Methodist University, Dallas, TX 75275-0156"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Southern Methodist University, Dallas, TX 75275-0156","institution_ids":["https://openalex.org/I178169726"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042712690","display_name":"Daniel R. Reynolds","orcid":"https://orcid.org/0000-0002-0911-7841"},"institutions":[{"id":"https://openalex.org/I178169726","display_name":"Southern Methodist University","ror":"https://ror.org/042tdr378","country_code":"US","type":"education","lineage":["https://openalex.org/I178169726"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel R. Reynolds","raw_affiliation_strings":["Department of Mathematics, Southern Methodist University, Dallas, TX 75275-0156"],"raw_orcid":"https://orcid.org/0000-0002-0911-7841","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Southern Methodist University, Dallas, TX 75275-0156","institution_ids":["https://openalex.org/I178169726"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5069156178"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9609,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.67303453,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"44","issue":"5","first_page":"A3265","last_page":"A3289"},"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":0.9997000098228455,"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":0.9986000061035156,"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/mathematics","display_name":"Mathematics","score":0.7995136976242065},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6705819368362427},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6199856996536255},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5837141871452332},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.5723077654838562},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.553806483745575},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.514241635799408},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4677961468696594},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.45891934633255005},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4412974715232849},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.417793333530426},{"id":"https://openalex.org/keywords/stiff-equation","display_name":"Stiff equation","score":0.41157686710357666},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.38450130820274353},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22094416618347168}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7995136976242065},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6705819368362427},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6199856996536255},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5837141871452332},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.5723077654838562},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.553806483745575},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.514241635799408},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4677961468696594},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.45891934633255005},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4412974715232849},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.417793333530426},{"id":"https://openalex.org/C43012357","wikidata":"https://www.wikidata.org/wiki/Q29744","display_name":"Stiff equation","level":3,"score":0.41157686710357666},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38450130820274353},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22094416618347168},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/21m1439481","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1439481","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2106.05385","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2106.05385","pdf_url":"https://arxiv.org/pdf/2106.05385","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"pmh:oai:osti.gov:1903121","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/1903121","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"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":null},{"id":"pmh:oai:osti.gov:1991759","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/1991759","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"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":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2106.05385","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2106.05385","pdf_url":"https://arxiv.org/pdf/2106.05385","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1542542466","display_name":null,"funder_award_id":"DMS-2012022","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4850031528","display_name":null,"funder_award_id":"DE-SC0021354","funder_id":"https://openalex.org/F4320338286","funder_display_name":"Lawrence Livermore National Laboratory"},{"id":"https://openalex.org/G6900540113","display_name":null,"funder_award_id":"DE-SC0021354","funder_id":"https://openalex.org/F4320337506","funder_display_name":"Advanced Scientific Computing Research"},{"id":"https://openalex.org/G7194819940","display_name":null,"funder_award_id":"DE-SC0021354","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G7471227859","display_name":"New Advanced Time Integration Methods for Multiphysics Systems and Applications","funder_award_id":"2012022","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G947473801","display_name":null,"funder_award_id":"B626484","funder_id":"https://openalex.org/F4320338286","funder_display_name":"Lawrence Livermore National Laboratory"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320332359","display_name":"Office of Science","ror":"https://ror.org/00mmn6b08"},{"id":"https://openalex.org/F4320337506","display_name":"Advanced Scientific Computing Research","ror":"https://ror.org/0012c7r22"},{"id":"https://openalex.org/F4320338286","display_name":"Lawrence Livermore National Laboratory","ror":"https://ror.org/041nk4h53"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W81600562","https://openalex.org/W1527296550","https://openalex.org/W1543750907","https://openalex.org/W1592415565","https://openalex.org/W1606157354","https://openalex.org/W1964391919","https://openalex.org/W1976371110","https://openalex.org/W1990615614","https://openalex.org/W1991962363","https://openalex.org/W1992011181","https://openalex.org/W1995504856","https://openalex.org/W2042388195","https://openalex.org/W2042875514","https://openalex.org/W2049161806","https://openalex.org/W2075304948","https://openalex.org/W2077852010","https://openalex.org/W2085471512","https://openalex.org/W2151777635","https://openalex.org/W2286249615","https://openalex.org/W2547560594","https://openalex.org/W2886551796","https://openalex.org/W2919764494","https://openalex.org/W2978349899","https://openalex.org/W2981874692","https://openalex.org/W3017850890","https://openalex.org/W3027336709","https://openalex.org/W3047743574","https://openalex.org/W3125249484","https://openalex.org/W3125331087","https://openalex.org/W3198390400","https://openalex.org/W4245463005","https://openalex.org/W4300831640"],"related_works":["https://openalex.org/W2012580470","https://openalex.org/W1998030649","https://openalex.org/W1569440961","https://openalex.org/W248048712","https://openalex.org/W3134445446","https://openalex.org/W2394270380","https://openalex.org/W2373832468","https://openalex.org/W135648373","https://openalex.org/W2059261580","https://openalex.org/W2791404322"],"abstract_inverted_index":{"In":[0,74],"this":[1],"paper":[2],"we":[3,89],"propose":[4],"a":[5,55],"novel":[6],"class":[7],"of":[8,14,17,33,51,57,86,94,102,130],"methods":[9,25,82,96,111,132],"for":[10],"high-order":[11,137],"accurate":[12],"integration":[13],"multirate":[15,27,45,110,138],"systems":[16],"ordinary":[18],"differential":[19],"equation":[20],"initial-value":[21,60,71],"problems.":[22],"The":[23],"proposed":[24],"construct":[26,80],"schemes":[28,101],"by":[29],"approximating":[30],"the":[31,52,128],"action":[32],"matrix":[34],"$\\varphi$":[35],"functions":[36],"within":[37],"explicit":[38],"exponential":[39],"Rosenbrock":[40],"(ExpRB)":[41],"methods,":[42,88],"thereby":[43],"called":[44],"ExpRB":[46,87],"(MERB)":[47],"methods.":[48,139],"They":[49],"consist":[50],"solution":[53],"to":[54,76,79,112,119,126],"sequence":[56],"modified":[58],"\u201cfast\u201d":[59],"problems,":[61],"which":[62],"may":[63],"themselves":[64],"be":[65],"approximated":[66],"through":[67,105],"subcycling":[68],"any":[69],"desired":[70],"problem":[72],"solver.":[73],"addition":[75],"proving":[77],"how":[78],"MERB":[81,100,131],"from":[83],"certain":[84],"classes":[85],"provide":[90],"rigorous":[91],"convergence":[92,123],"analysis":[93],"these":[95,121],"and":[97,125],"derive":[98],"efficient":[99],"orders":[103],"2":[104],"6":[106],"(the":[107],"highest-order":[108],"infinitesimal":[109],"date).":[113],"We":[114],"then":[115],"present":[116],"numerical":[117],"simulations":[118],"confirm":[120],"theoretical":[122],"rates":[124],"compare":[127],"efficiency":[129],"against":[133],"other":[134],"recently":[135],"introduced":[136]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2}],"updated_date":"2026-05-11T08:15:01.531666","created_date":"2025-10-10T00:00:00"}
