{"id":"https://openalex.org/W2164727697","doi":"https://doi.org/10.1137/040606995","title":"Explicit, Time Reversible, Adaptive Step Size Control","display_name":"Explicit, Time Reversible, Adaptive Step Size Control","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2164727697","doi":"https://doi.org/10.1137/040606995","mag":"2164727697"},"language":"en","primary_location":{"id":"doi:10.1137/040606995","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040606995","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":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://archive-ouverte.unige.ch/unige:12120","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026173495","display_name":"Ernst Hairer","orcid":"https://orcid.org/0000-0001-5057-2654"},"institutions":[{"id":"https://openalex.org/I114457229","display_name":"University of Geneva","ror":"https://ror.org/01swzsf04","country_code":"CH","type":"education","lineage":["https://openalex.org/I114457229"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Ernst Hairer","raw_affiliation_strings":["University of GENEVA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of GENEVA","institution_ids":["https://openalex.org/I114457229"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085498434","display_name":"Gustaf S\u00f6derlind","orcid":"https://orcid.org/0000-0003-3559-960X"},"institutions":[{"id":"https://openalex.org/I4210093057","display_name":"Faculty (United Kingdom)","ror":"https://ror.org/00qpxe165","country_code":"GB","type":"company","lineage":["https://openalex.org/I4210093057"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Gustaf S\u00f6derlind","raw_affiliation_strings":["Mathematics (Faculty of Engineering)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics (Faculty of Engineering)","institution_ids":["https://openalex.org/I4210093057"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.1097,"has_fulltext":false,"cited_by_count":63,"citation_normalized_percentile":{"value":0.96500413,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"26","issue":"6","first_page":"1838","last_page":"1851"},"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":0.9927999973297119,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9853000044822693,"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/integrator","display_name":"Integrator","score":0.7818276882171631},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7587934732437134},{"id":"https://openalex.org/keywords/verlet-integration","display_name":"Verlet integration","score":0.6725883483886719},{"id":"https://openalex.org/keywords/integrable-system","display_name":"Integrable system","score":0.47593238949775696},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.44506993889808655},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43457871675491333},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.43361160159111023},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.41323018074035645},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.37064796686172485},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34213244915008545},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23972684144973755},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.19335627555847168},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15647470951080322},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.11333519220352173}],"concepts":[{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.7818276882171631},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7587934732437134},{"id":"https://openalex.org/C45600393","wikidata":"https://www.wikidata.org/wiki/Q2984997","display_name":"Verlet integration","level":3,"score":0.6725883483886719},{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.47593238949775696},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.44506993889808655},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43457871675491333},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.43361160159111023},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.41323018074035645},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.37064796686172485},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34213244915008545},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23972684144973755},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.19335627555847168},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15647470951080322},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.11333519220352173},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C147597530","wikidata":"https://www.wikidata.org/wiki/Q369472","display_name":"Computational chemistry","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/C59593255","wikidata":"https://www.wikidata.org/wiki/Q901663","display_name":"Molecular dynamics","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/040606995","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040606995","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:unige.ch:unige:12120","is_oa":true,"landing_page_url":"https://archive-ouverte.unige.ch/unige:12120","pdf_url":null,"source":{"id":"https://openalex.org/S4306402259","display_name":"Archive ouverte UNIGE (University of Geneva)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I114457229","host_organization_name":"University of Geneva","host_organization_lineage":["https://openalex.org/I114457229"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"ISSN: 1064-8275","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.91.9571","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.91.9571","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.unige.ch/~hairer/preprints/revstep.pdf","raw_type":"text"},{"id":"pmh:oai:lup.lub.lu.se:b23073b3-306e-45c7-ba55-884a7eac889e","is_oa":false,"landing_page_url":"https://lup.lub.lu.se/record/226528","pdf_url":null,"source":{"id":"https://openalex.org/S4306400536","display_name":"Lund University Publications (Lund University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I187531555","host_organization_name":"Lund University","host_organization_lineage":["https://openalex.org/I187531555"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 1064-8275","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:unige.ch:unige:12120","is_oa":true,"landing_page_url":"https://archive-ouverte.unige.ch/unige:12120","pdf_url":null,"source":{"id":"https://openalex.org/S4306402259","display_name":"Archive ouverte UNIGE (University of Geneva)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I114457229","host_organization_name":"University of Geneva","host_organization_lineage":["https://openalex.org/I114457229"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"ISSN: 1064-8275","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"display_name":"Affordable and clean energy","score":0.8700000047683716,"id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1544770838","https://openalex.org/W1554968945","https://openalex.org/W1884654681","https://openalex.org/W1969140784","https://openalex.org/W1974689218","https://openalex.org/W2003351322","https://openalex.org/W2012420344","https://openalex.org/W2089974659","https://openalex.org/W2108371414","https://openalex.org/W2147351090","https://openalex.org/W2947056241"],"related_works":["https://openalex.org/W3017231357","https://openalex.org/W4386963729","https://openalex.org/W2190914950","https://openalex.org/W3098407907","https://openalex.org/W88263287","https://openalex.org/W3102212431","https://openalex.org/W4205967490","https://openalex.org/W4289288125","https://openalex.org/W2900876247","https://openalex.org/W2163206513"],"abstract_inverted_index":{"Adaptive":[0],"step":[1,14,46,61],"size":[2,15,47],"control":[3,16],"is":[4,17,25,64],"difficult":[5],"to":[6],"combine":[7],"with":[8,28],"geometric":[9,51],"numerical":[10,52],"integration.":[11],"As":[12],"classical":[13],"based":[18],"on":[19],"\"past\"":[20],"information":[21],"only,":[22],"time":[23],"symmetry":[24],"destroyed":[26],"and":[27,66,72,122],"it":[29],"the":[30,34,56,83,95,103],"qualitative":[31],"properties":[32],"of":[33],"method.":[35,58],"In":[36],"this":[37],"paper":[38],"we":[39,80],"develop":[40],"completely":[41],"explicit,":[42],"reversible,":[43],"symmetry-preserving,":[44],"adaptive":[45,85],"selection":[48],"algorithms":[49],"for":[50,98],"integrators":[53],"such":[54],"as":[55,108],"St\u00f6rmer--Verlet":[57],"A":[59],"new":[60],"density":[62],"controller":[63],"proposed":[65],"analyzed":[67],"using":[68],"backward":[69],"error":[70],"analysis":[71],"reversible":[73,78],"perturbation":[74],"theory.":[75],"For":[76],"integrable":[77],"systems":[79],"show":[81],"that":[82,109],"resulting":[84],"method":[86],"nearly":[87],"preserves":[88],"all":[89],"action":[90],"variables":[91],"and,":[92],"in":[93],"particular,":[94],"total":[96],"energy":[97],"Hamiltonian":[99],"systems.":[100],"It":[101],"has":[102],"same":[104],"excellent":[105],"long-term":[106],"behavior":[107],"obtained":[110],"when":[111],"constant":[112],"steps":[113],"are":[114,124],"used.":[115],"With":[116],"variable":[117],"steps,":[118],"however,":[119],"both":[120],"accuracy":[121],"efficiency":[123],"greatly":[125],"improved.":[126]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":5}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}
