{"id":"https://openalex.org/W2032090338","doi":"https://doi.org/10.1137/s0036142901395588","title":"Numerical Methods for Stochastic Systems Preserving Symplectic Structure","display_name":"Numerical Methods for Stochastic Systems Preserving Symplectic Structure","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2032090338","doi":"https://doi.org/10.1137/s0036142901395588","mag":"2032090338"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142901395588","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142901395588","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":true,"oa_status":"green","oa_url":"http://elar.urfu.ru/handle/10995/111188","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066964804","display_name":"Grigori N. Milstein","orcid":null},"institutions":[{"id":"https://openalex.org/I4210092021","display_name":"Weierstrass Institute for Applied Analysis and Stochastics","ror":"https://ror.org/00h1x4t21","country_code":"DE","type":"facility","lineage":["https://openalex.org/I315704651","https://openalex.org/I4210092021"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"G. N. Milstein","raw_affiliation_strings":["Weierstra\u00df-Institut f\u00fcr Angewandte Analysis und Stochastik, Mohrenstr. 39, D-10117 Berlin, Germany","Department of Mathematics, Ural State University, Lenin Str. 51, 620083 Ekaterinburg, Russia"],"affiliations":[{"raw_affiliation_string":"Weierstra\u00df-Institut f\u00fcr Angewandte Analysis und Stochastik, Mohrenstr. 39, D-10117 Berlin, Germany","institution_ids":["https://openalex.org/I4210092021"]},{"raw_affiliation_string":"Department of Mathematics, Ural State University, Lenin Str. 51, 620083 Ekaterinburg, Russia","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006056729","display_name":"Yu. M. Repin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yu. M. Repin","raw_affiliation_strings":["Department of Mathematics, Ural State University, Lenin Str. 51, 620083 Ekaterinburg, Russia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Ural State University, Lenin Str. 51, 620083 Ekaterinburg, Russia","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081243775","display_name":"M. V. Tretyakov","orcid":"https://orcid.org/0000-0002-7929-9046"},"institutions":[{"id":"https://openalex.org/I97429440","display_name":"University of Wales","ror":"https://ror.org/01se4f844","country_code":"GB","type":"education","lineage":["https://openalex.org/I97429440"]},{"id":"https://openalex.org/I39586589","display_name":"Swansea University","ror":"https://ror.org/053fq8t95","country_code":"GB","type":"education","lineage":["https://openalex.org/I39586589"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"M. V. Tretyakov","raw_affiliation_strings":["Department of Mathematics, University of Wales Swansea, Swansea SA2 8PP, UK"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wales Swansea, Swansea SA2 8PP, UK","institution_ids":["https://openalex.org/I39586589","https://openalex.org/I97429440"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5066964804"],"corresponding_institution_ids":["https://openalex.org/I4210092021"],"apc_list":null,"apc_paid":null,"fwci":3.646,"has_fulltext":false,"cited_by_count":189,"citation_normalized_percentile":{"value":0.92484472,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"40","issue":"4","first_page":"1583","last_page":"1604"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9988999962806702,"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":0.9988999962806702,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9865000247955322,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.974399983882904,"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/symplectic-geometry","display_name":"Symplectic geometry","score":0.9043184518814087},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7981451749801636},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.6868758797645569},{"id":"https://openalex.org/keywords/symplectic-integrator","display_name":"Symplectic integrator","score":0.6682837009429932},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.554575502872467},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5450412034988403},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.44411715865135193},{"id":"https://openalex.org/keywords/phase-space","display_name":"Phase space","score":0.4233665466308594},{"id":"https://openalex.org/keywords/integrator","display_name":"Integrator","score":0.42108353972435},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2572707533836365},{"id":"https://openalex.org/keywords/symplectic-manifold","display_name":"Symplectic manifold","score":0.23356258869171143},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1356443464756012}],"concepts":[{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.9043184518814087},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7981451749801636},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.6868758797645569},{"id":"https://openalex.org/C207646825","wikidata":"https://www.wikidata.org/wiki/Q7661847","display_name":"Symplectic integrator","level":4,"score":0.6682837009429932},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.554575502872467},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5450412034988403},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.44411715865135193},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.4233665466308594},{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.42108353972435},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2572707533836365},{"id":"https://openalex.org/C130190758","wikidata":"https://www.wikidata.org/wiki/Q1064500","display_name":"Symplectic manifold","level":3,"score":0.23356258869171143},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1356443464756012},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/s0036142901395588","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142901395588","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:CiteSeerX.psu:10.1.1.598.1816","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.598.1816","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.le.ac.uk/PEOPLE/mt72/39558.pdf","raw_type":"text"},{"id":"pmh:oai:elar.urfu.ru:10995/111188","is_oa":true,"landing_page_url":"http://elar.urfu.ru/handle/10995/111188","pdf_url":null,"source":{"id":"https://openalex.org/S4306401522","display_name":"Electronic scientific archive of UrFU (Ural Federal University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130823665","host_organization_name":"Ural Federal University","host_organization_lineage":["https://openalex.org/I130823665"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"info:eu-repo/semantics/submittedVersion"},{"id":"pmh:oai:elar.urfu.ru:10995/112183","is_oa":true,"landing_page_url":"http://elar.urfu.ru/handle/10995/112183","pdf_url":null,"source":{"id":"https://openalex.org/S4306401522","display_name":"Electronic scientific archive of UrFU (Ural Federal University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130823665","host_organization_name":"Ural Federal University","host_organization_lineage":["https://openalex.org/I130823665"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Europhys. Lett.","raw_type":"Article"},{"id":"pmh:oai:lra.le.ac.uk:2381/26890","is_oa":false,"landing_page_url":"http://hdl.handle.net/2381/26890","pdf_url":null,"source":{"id":"https://openalex.org/S4306402365","display_name":"Leicester Research Archive (University of Leicester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I153648349","host_organization_name":"University of Leicester","host_organization_lineage":["https://openalex.org/I153648349"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Scopus","raw_type":"Journal Article"}],"best_oa_location":{"id":"pmh:oai:elar.urfu.ru:10995/111188","is_oa":true,"landing_page_url":"http://elar.urfu.ru/handle/10995/111188","pdf_url":null,"source":{"id":"https://openalex.org/S4306401522","display_name":"Electronic scientific archive of UrFU (Ural Federal University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130823665","host_organization_name":"Ural Federal University","host_organization_lineage":["https://openalex.org/I130823665"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"info:eu-repo/semantics/submittedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321079","display_name":"Russian Foundation for Basic Research","ror":"https://ror.org/02mh1ke95"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W194549626","https://openalex.org/W1575104486","https://openalex.org/W1607503834","https://openalex.org/W1971274873","https://openalex.org/W1995504856","https://openalex.org/W2017032949","https://openalex.org/W2019176751","https://openalex.org/W2042388195","https://openalex.org/W2045701663","https://openalex.org/W2078916875","https://openalex.org/W2084367325","https://openalex.org/W2124176552","https://openalex.org/W2126479355","https://openalex.org/W2148437017","https://openalex.org/W4231021340","https://openalex.org/W4231366763","https://openalex.org/W4255754126"],"related_works":["https://openalex.org/W2005694504","https://openalex.org/W1994054117","https://openalex.org/W2953100675","https://openalex.org/W2952306674","https://openalex.org/W2064282017","https://openalex.org/W2027000851","https://openalex.org/W2165812552","https://openalex.org/W25827740","https://openalex.org/W4298036990","https://openalex.org/W4302160352"],"abstract_inverted_index":{"Stochastic":[0],"Hamiltonian":[1],"systems":[2,48,79],"with":[3,29,80,104],"multiplicative":[4],"noise,":[5],"phase":[6],"flows":[7],"of":[8,42,52,69,85,93],"which":[9],"preserve":[10],"symplectic":[11,17,70,96],"structure,":[12],"are":[13,37,60,88],"considered.":[14],"To":[15],"construct":[16],"methods":[18,45,97],"for":[19,46],"such":[20],"systems,":[21],"sufficiently":[22],"general":[23],"fully":[24,43,57],"implicit":[25,44,58],"schemes,":[26],"i.e.,":[27],"schemes":[28,59],"implicitness":[30],"both":[31],"in":[32,55,102],"deterministic":[33],"and":[34],"stochastic":[35,47],"terms,":[36],"needed.":[38],"A":[39,67],"new":[40],"class":[41],"is":[49,72,76],"proposed.":[50],"Increments":[51],"Wiener":[53],"processes":[54],"these":[56],"substituted":[61],"by":[62],"some":[63],"truncated":[64],"random":[65],"variables.":[66],"number":[68],"integrators":[71],"constructed.":[73],"Special":[74],"attention":[75],"paid":[77],"to":[78],"separable":[81],"Hamiltonians.":[82],"Some":[83],"results":[84],"numerical":[86],"experiments":[87],"presented.":[89],"They":[90],"demonstrate":[91],"superiority":[92],"the":[94],"proposed":[95],"over":[98],"very":[99],"long":[100],"times":[101],"comparison":[103],"nonsymplectic":[105],"ones.":[106]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":14},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":16},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":13},{"year":2019,"cited_by_count":12},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":13},{"year":2016,"cited_by_count":13},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":5}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
