{"id":"https://openalex.org/W2090704787","doi":"https://doi.org/10.1137/040611434","title":"Explicit Exponential Runge--Kutta Methods for Semilinear Parabolic Problems","display_name":"Explicit Exponential Runge--Kutta Methods for Semilinear Parabolic Problems","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2090704787","doi":"https://doi.org/10.1137/040611434","mag":"2090704787"},"language":"en","primary_location":{"id":"doi:10.1137/040611434","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040611434","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","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5445/ir/1000042061","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013995544","display_name":"Marlis Hochbruck","orcid":"https://orcid.org/0000-0002-5968-0480"},"institutions":[{"id":"https://openalex.org/I44260953","display_name":"Heinrich Heine University D\u00fcsseldorf","ror":"https://ror.org/024z2rq82","country_code":"DE","type":"education","lineage":["https://openalex.org/I44260953"]},{"id":"https://openalex.org/I190249584","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659","country_code":"AT","type":"education","lineage":["https://openalex.org/I190249584"]}],"countries":["AT","DE"],"is_corresponding":true,"raw_author_name":"Marlis Hochbruck","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Universit\u00e4t Innsbruck, Technikerstr. 13, A-6020 Innsbruck, Austria","Mathematisches Institut, Heinrich-Heine Universit\u00e4t D\u00fcsseldorf, Universit\u00e4tsstr. 1, D-40225 D\u00fcsseldorf, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Universit\u00e4t Innsbruck, Technikerstr. 13, A-6020 Innsbruck, Austria","institution_ids":["https://openalex.org/I190249584"]},{"raw_affiliation_string":"Mathematisches Institut, Heinrich-Heine Universit\u00e4t D\u00fcsseldorf, Universit\u00e4tsstr. 1, D-40225 D\u00fcsseldorf, Germany","institution_ids":["https://openalex.org/I44260953"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047834422","display_name":"Alexander Ostermann","orcid":"https://orcid.org/0000-0003-0194-2481"},"institutions":[{"id":"https://openalex.org/I190249584","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659","country_code":"AT","type":"education","lineage":["https://openalex.org/I190249584"]},{"id":"https://openalex.org/I44260953","display_name":"Heinrich Heine University D\u00fcsseldorf","ror":"https://ror.org/024z2rq82","country_code":"DE","type":"education","lineage":["https://openalex.org/I44260953"]}],"countries":["AT","DE"],"is_corresponding":false,"raw_author_name":"Alexander Ostermann","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Universit\u00e4t Innsbruck, Technikerstr. 13, A-6020 Innsbruck, Austria","Mathematisches Institut, Heinrich-Heine Universit\u00e4t D\u00fcsseldorf, Universit\u00e4tsstr. 1, D-40225 D\u00fcsseldorf, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Universit\u00e4t Innsbruck, Technikerstr. 13, A-6020 Innsbruck, Austria","institution_ids":["https://openalex.org/I190249584"]},{"raw_affiliation_string":"Mathematisches Institut, Heinrich-Heine Universit\u00e4t D\u00fcsseldorf, Universit\u00e4tsstr. 1, D-40225 D\u00fcsseldorf, Germany","institution_ids":["https://openalex.org/I44260953"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5013995544"],"corresponding_institution_ids":["https://openalex.org/I190249584","https://openalex.org/I44260953"],"apc_list":null,"apc_paid":null,"fwci":16.3842,"has_fulltext":false,"cited_by_count":436,"citation_normalized_percentile":{"value":0.99483976,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"43","issue":"3","first_page":"1069","last_page":"1090"},"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9993000030517578,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9993000030517578,"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/mathematics","display_name":"Mathematics","score":0.849318265914917},{"id":"https://openalex.org/keywords/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.8411725759506226},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.7164333462715149},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.610222578048706},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5706986784934998},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5511531233787537},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.531507670879364},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.485139936208725},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.4274408221244812},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.4273838996887207},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.4155122637748718},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4073154330253601},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.39548617601394653},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.2553732395172119},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08327370882034302}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.849318265914917},{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.8411725759506226},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.7164333462715149},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.610222578048706},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5706986784934998},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5511531233787537},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.531507670879364},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.485139936208725},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.4274408221244812},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.4273838996887207},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.4155122637748718},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4073154330253601},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.39548617601394653},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2553732395172119},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08327370882034302},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/040611434","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040611434","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"},{"id":"pmh:oai:EVASTAR-Karlsruhe.de:1000042061","is_oa":false,"landing_page_url":"https://publikationen.bibliothek.kit.edu/1000042061","pdf_url":null,"source":{"id":"https://openalex.org/S4306401992","display_name":"Repository KITopen (Karlsruhe Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I102335020","host_organization_name":"Karlsruhe Institute of Technology","host_organization_lineage":["https://openalex.org/I102335020"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis, 43 (3), 1069-1090","raw_type":"doc-type:article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.561.5501","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.561.5501","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://techmath.uibk.ac.at/mathematik/publikationen/04-4.pdf","raw_type":"text"},{"id":"doi:10.5445/ir/1000042061","is_oa":true,"landing_page_url":"https://doi.org/10.5445/ir/1000042061","pdf_url":null,"source":{"id":"https://openalex.org/S7407052948","display_name":"KITopen","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.5445/ir/1000042061","is_oa":true,"landing_page_url":"https://doi.org/10.5445/ir/1000042061","pdf_url":null,"source":{"id":"https://openalex.org/S7407052948","display_name":"KITopen","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W85500490","https://openalex.org/W586282074","https://openalex.org/W1527296550","https://openalex.org/W1540580484","https://openalex.org/W1560060148","https://openalex.org/W1970532716","https://openalex.org/W1970906109","https://openalex.org/W1978652608","https://openalex.org/W2002187166","https://openalex.org/W2005061077","https://openalex.org/W2010652522","https://openalex.org/W2027319740","https://openalex.org/W2032171614","https://openalex.org/W2039880089","https://openalex.org/W2042388195","https://openalex.org/W2049165066","https://openalex.org/W2067136705","https://openalex.org/W2075247318","https://openalex.org/W2075857446","https://openalex.org/W2092112892","https://openalex.org/W2095219532","https://openalex.org/W2106565812","https://openalex.org/W2139120673","https://openalex.org/W2142895119","https://openalex.org/W2164743984","https://openalex.org/W2224436197","https://openalex.org/W4251840481","https://openalex.org/W4255754126","https://openalex.org/W4302061159"],"related_works":["https://openalex.org/W3185235544","https://openalex.org/W4206768127","https://openalex.org/W2911623553","https://openalex.org/W2999850718","https://openalex.org/W3014042903","https://openalex.org/W4287548472","https://openalex.org/W3087130726","https://openalex.org/W2550125528","https://openalex.org/W988753663","https://openalex.org/W2019053975"],"abstract_inverted_index":{"Abstract.":[0],"The":[1,21],"aim":[2],"of":[3,17,31,48,62,75,81,93,132],"this":[4,149],"paper":[5,64],"is":[6,23,140],"to":[7,106],"analyze":[8,111],"explicit":[9],"exponential":[10,55],"Runge-Kutta":[11,56],"methods":[12,104,112,121,166],"for":[13,54,97,103],"the":[14,49,59,67,73,76,82,91,118,133],"time":[15],"integration":[16],"semilinear":[18],"parabolic":[19,98],"problems.":[20,99],"analysis":[22],"performed":[24],"in":[25,66,79,117,152,155],"an":[26,137],"abstract":[27],"Banach":[28],"space":[29],"framework":[30],"sectorial":[32],"operators":[33],"and":[34,45,109],"locally":[35],"Lipschitz":[36],"continuous":[37],"nonlinearities.":[38],"We":[39,100,142],"commence":[40],"by":[41],"giving":[42],"a":[43],"new":[44,86,134,161],"short":[46],"derivation":[47],"classical":[50,123],"(nonsti\u00ae)":[51],"order":[52,87,107,124,138,150,172],"conditions":[53,88],"methods,":[57],"but":[58,126],"main":[60],"interest":[61],"our":[63,94,160],"lies":[65],"sti":[68],"\u00ae":[69],"case.":[70],"By":[71],"expanding":[72],"errors":[74],"numerical":[77,144],"method":[78],"terms":[80],"solution,":[83],"we":[84,110,163],"derive":[85],"that":[89,113,148,167],"form":[90],"basis":[92],"error":[95],"bounds":[96],"show":[101,147],"convergence":[102],"up":[105],"four":[108],"were":[114],"recently":[115],"presented":[116],"literature.":[119],"These":[120],"have":[122],"four,":[125],"they":[127],"do":[128,168],"not":[129,169],"satisfy":[130],"some":[131],"conditions.":[135],"Therefore,":[136],"reduction":[139,151],"expected.":[141],"present":[143],"experiments":[145],"which":[146],"fact":[153],"arises":[154],"practical":[156],"examples.":[157],"Based":[158],"on":[159],"conditions,":[162],"\u00afnally":[164],"construct":[165],"su\u00aeer":[170],"from":[171],"reduction.":[173],"1.":[174],"Introduction.":[175],"Motivated":[176]},"counts_by_year":[{"year":2026,"cited_by_count":10},{"year":2025,"cited_by_count":33},{"year":2024,"cited_by_count":40},{"year":2023,"cited_by_count":37},{"year":2022,"cited_by_count":21},{"year":2021,"cited_by_count":36},{"year":2020,"cited_by_count":37},{"year":2019,"cited_by_count":18},{"year":2018,"cited_by_count":22},{"year":2017,"cited_by_count":21},{"year":2016,"cited_by_count":21},{"year":2015,"cited_by_count":19},{"year":2014,"cited_by_count":13},{"year":2013,"cited_by_count":15},{"year":2012,"cited_by_count":14}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
