{"id":"https://openalex.org/W1134214559","doi":"https://doi.org/10.1137/151005798","title":"Steady State and Sign Preserving Semi-Implicit Runge--Kutta Methods for ODEs with Stiff Damping Term","display_name":"Steady State and Sign Preserving Semi-Implicit Runge--Kutta Methods for ODEs with Stiff Damping Term","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1134214559","doi":"https://doi.org/10.1137/151005798","mag":"1134214559"},"language":"en","primary_location":{"id":"doi:10.1137/151005798","is_oa":false,"landing_page_url":"https://doi.org/10.1137/151005798","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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/A5045555983","display_name":"Alina Chertock","orcid":"https://orcid.org/0000-0003-4978-1314"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Alina Chertock","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082990660","display_name":"Shumo Cui","orcid":"https://orcid.org/0000-0001-6686-6876"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shumo Cui","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091293976","display_name":"Alexander Kurganov","orcid":"https://orcid.org/0000-0003-0231-986X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alexander Kurganov","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5032532102","display_name":"Tong Wu","orcid":"https://orcid.org/0000-0002-3748-063X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tong Wu","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5045555983"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.4247,"has_fulltext":false,"cited_by_count":48,"citation_normalized_percentile":{"value":0.95965944,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"53","issue":"4","first_page":"2008","last_page":"2029"},"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9998000264167786,"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"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9991000294685364,"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/ode","display_name":"Ode","score":0.9016053080558777},{"id":"https://openalex.org/keywords/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.8618313670158386},{"id":"https://openalex.org/keywords/l-stability","display_name":"L-stability","score":0.8166478872299194},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7922780513763428},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6884270906448364},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6419299840927124},{"id":"https://openalex.org/keywords/stiff-equation","display_name":"Stiff equation","score":0.6370244026184082},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.5002562999725342},{"id":"https://openalex.org/keywords/backward-differentiation-formula","display_name":"Backward differentiation formula","score":0.4913136065006256},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4877529740333557},{"id":"https://openalex.org/keywords/explicit-and-implicit-methods","display_name":"Explicit and implicit methods","score":0.4770747423171997},{"id":"https://openalex.org/keywords/sign","display_name":"Sign (mathematics)","score":0.4685051739215851},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4674224555492401},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.45442062616348267},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.42932188510894775},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3917899429798126},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.3838343620300293},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.3428748846054077},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3410225212574005},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.16349822282791138},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.15300294756889343},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1316682994365692},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10880208015441895}],"concepts":[{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.9016053080558777},{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.8618313670158386},{"id":"https://openalex.org/C165242687","wikidata":"https://www.wikidata.org/wiki/Q277932","display_name":"L-stability","level":5,"score":0.8166478872299194},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7922780513763428},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6884270906448364},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6419299840927124},{"id":"https://openalex.org/C43012357","wikidata":"https://www.wikidata.org/wiki/Q29744","display_name":"Stiff equation","level":3,"score":0.6370244026184082},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.5002562999725342},{"id":"https://openalex.org/C152522140","wikidata":"https://www.wikidata.org/wiki/Q795746","display_name":"Backward differentiation formula","level":5,"score":0.4913136065006256},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4877529740333557},{"id":"https://openalex.org/C149393637","wikidata":"https://www.wikidata.org/wiki/Q5421265","display_name":"Explicit and implicit methods","level":5,"score":0.4770747423171997},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.4685051739215851},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4674224555492401},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.45442062616348267},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.42932188510894775},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3917899429798126},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3838343620300293},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.3428748846054077},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3410225212574005},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.16349822282791138},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.15300294756889343},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1316682994365692},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10880208015441895},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/151005798","is_oa":false,"landing_page_url":"https://doi.org/10.1137/151005798","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/6","display_name":"Clean water and sanitation","score":0.75}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W126643224","https://openalex.org/W644636885","https://openalex.org/W1486816047","https://openalex.org/W1559129386","https://openalex.org/W1973481688","https://openalex.org/W1991884722","https://openalex.org/W2005665126","https://openalex.org/W2016699328","https://openalex.org/W2017184164","https://openalex.org/W2020863487","https://openalex.org/W2038063432","https://openalex.org/W2054420328","https://openalex.org/W2064480181","https://openalex.org/W2072052012","https://openalex.org/W2093711514","https://openalex.org/W2096894484","https://openalex.org/W2100520965","https://openalex.org/W2116729868","https://openalex.org/W2128618499","https://openalex.org/W2133429431","https://openalex.org/W2246415295","https://openalex.org/W2963401669","https://openalex.org/W3010292040"],"related_works":["https://openalex.org/W2088005785","https://openalex.org/W2278428637","https://openalex.org/W797453289","https://openalex.org/W2378531610","https://openalex.org/W2068100081","https://openalex.org/W2185332433","https://openalex.org/W130803118","https://openalex.org/W2047347911","https://openalex.org/W10203595","https://openalex.org/W3048000545"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"develop":[4],"a":[5,91,114,119,163],"family":[6],"of":[7,15,27,39,51,65,78,95,105,121,127,145],"second-order":[8],"semi-implicit":[9,71,110],"time":[10,57],"integration":[11],"methods":[12,30,72,85,111],"for":[13],"systems":[14],"ordinary":[16],"differential":[17],"equations":[18,131],"(ODEs)":[19],"with":[20,132],"stiff":[21,99,133],"damping":[22],"term.":[23,135],"The":[24,69,136],"important":[25,156],"feature":[26],"the":[28,33,42,49,52,56,62,66,76,103,106,125,128,143,146],"new":[29,70],"resides":[31],"in":[32,158],"fact":[34],"that":[35,142],"they":[36],"are":[37,73,87],"capable":[38],"exactly":[40,151],"preserving":[41,82],"steady":[43],"states":[44],"as":[45,47],"well":[46],"maintaining":[48],"sign":[50],"computed":[53],"solution":[54],"under":[55],"step":[58],"restriction":[59],"determined":[60],"by":[61],"nonstiff":[63],"part":[64],"system":[67,120],"only.":[68],"based":[74,109],"on":[75,112],"modification":[77],"explicit":[79],"strong":[80],"stability":[81],"Runge--Kutta":[83],"(SSP-RK)":[84],"and":[86,98,118],"proven":[88],"to":[89,150],"have":[90],"formal":[92],"second":[93],"order":[94],"accuracy,":[96],"$A(\\alpha)$-stability,":[97],"decay.":[100],"We":[101],"illustrate":[102],"performance":[104],"proposed":[107],"SSP-RK":[108],"both":[113],"scalar":[115],"ODE":[116,148],"example":[117],"ODEs":[122],"arising":[123],"from":[124],"semi-discretization":[126],"shallow":[129],"water":[130],"friction":[134],"obtained":[137],"numerical":[138],"results":[139],"clearly":[140],"demonstrate":[141],"ability":[144],"introduced":[147],"solver":[149],"preserve":[152],"equilibria":[153],"plays":[154],"an":[155],"role":[157],"achieving":[159],"high":[160],"resolution":[161],"when":[162],"coarse":[164],"grid":[165],"is":[166],"used.":[167]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
