{"id":"https://openalex.org/W2090858114","doi":"https://doi.org/10.1137/050646032","title":"Numerical Methods for Second\u2010Order Stochastic Differential Equations","display_name":"Numerical Methods for Second\u2010Order Stochastic Differential Equations","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2090858114","doi":"https://doi.org/10.1137/050646032","mag":"2090858114"},"language":"en","primary_location":{"id":"doi:10.1137/050646032","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050646032","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003330950","display_name":"Kevin Burrage","orcid":"https://orcid.org/0000-0002-8111-1137"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kevin Burrage","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047725642","display_name":"I.J. Lenane","orcid":"https://orcid.org/0000-0002-2835-4201"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ian Lenane","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5022689831","display_name":"Grant Lythe","orcid":"https://orcid.org/0000-0001-7966-5571"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Grant Lythe","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.9253,"has_fulltext":false,"cited_by_count":145,"citation_normalized_percentile":{"value":0.90179816,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"29","issue":"1","first_page":"245","last_page":"264"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10466","display_name":"Meteorological Phenomena and Simulations","score":0.9926999807357788,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10466","display_name":"Meteorological Phenomena and Simulations","score":0.9926999807357788,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9887999892234802,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9876000285148621,"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":0.8798768520355225},{"id":"https://openalex.org/keywords/midpoint-method","display_name":"Midpoint method","score":0.6527436971664429},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.5569820404052734},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5499696731567383},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.49022895097732544},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4863291382789612},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4777368903160095},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4664560854434967},{"id":"https://openalex.org/keywords/midpoint","display_name":"Midpoint","score":0.45648595690727234},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.436975359916687},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4341368079185486},{"id":"https://openalex.org/keywords/multiplicative-noise","display_name":"Multiplicative noise","score":0.42633652687072754},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12246260046958923}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8798768520355225},{"id":"https://openalex.org/C85807060","wikidata":"https://www.wikidata.org/wiki/Q17103851","display_name":"Midpoint method","level":2,"score":0.6527436971664429},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.5569820404052734},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5499696731567383},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.49022895097732544},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4863291382789612},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4777368903160095},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4664560854434967},{"id":"https://openalex.org/C34130140","wikidata":"https://www.wikidata.org/wiki/Q1645406","display_name":"Midpoint","level":2,"score":0.45648595690727234},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.436975359916687},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4341368079185486},{"id":"https://openalex.org/C18015164","wikidata":"https://www.wikidata.org/wiki/Q6935000","display_name":"Multiplicative noise","level":5,"score":0.42633652687072754},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12246260046958923},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C84462506","wikidata":"https://www.wikidata.org/wiki/Q173142","display_name":"Digital signal processing","level":2,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C131021393","wikidata":"https://www.wikidata.org/wiki/Q7512759","display_name":"Signal transfer function","level":4,"score":0.0},{"id":"https://openalex.org/C13412647","wikidata":"https://www.wikidata.org/wiki/Q174948","display_name":"Analog signal","level":3,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","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":3,"locations":[{"id":"doi:10.1137/050646032","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050646032","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:CiteSeerX.psu:10.1.1.103.30","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.103.30","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.maths.leeds.ac.uk/~grant/BLL.pdf","raw_type":"text"},{"id":"pmh:oai:espace.library.uq.edu.au:UQ:128286","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306402388","display_name":"Queensland's institutional digital repository (The University of Queensland)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I165143802","host_organization_name":"The University of Queensland","host_organization_lineage":["https://openalex.org/I165143802"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W9124626","https://openalex.org/W1544770838","https://openalex.org/W1642251103","https://openalex.org/W1988053360","https://openalex.org/W1992880075","https://openalex.org/W1992881609","https://openalex.org/W2011436140","https://openalex.org/W2019092624","https://openalex.org/W2024167063","https://openalex.org/W2027578254","https://openalex.org/W2031290769","https://openalex.org/W2041902442","https://openalex.org/W2042388195","https://openalex.org/W2045386145","https://openalex.org/W2056854811","https://openalex.org/W2062709451","https://openalex.org/W2073658284","https://openalex.org/W2082618321","https://openalex.org/W2083164919","https://openalex.org/W2083763944","https://openalex.org/W2104049095","https://openalex.org/W2113913163","https://openalex.org/W2168958073","https://openalex.org/W2323178299"],"related_works":["https://openalex.org/W2072226187","https://openalex.org/W2391598905","https://openalex.org/W2330791370","https://openalex.org/W37565017","https://openalex.org/W2357395917","https://openalex.org/W2055023320","https://openalex.org/W3091779247","https://openalex.org/W2391440809","https://openalex.org/W2626449361","https://openalex.org/W1485125211"],"abstract_inverted_index":{"We":[0],"seek":[1],"numerical":[2],"methods":[3,64,109],"for":[4,15,25,57,63,88],"second\u2010order":[5,28],"stochastic":[6],"differential":[7],"equations":[8,29,112],"that":[9,81],"reproduce":[10],"the":[11,37,47,58,83,94,101,122],"stationary":[12,59],"density":[13,87],"accurately":[14],"all":[16,89],"values":[17,90],"of":[18,91],"damping.":[19],"A":[20,52],"complete":[21],"analysis":[22],"is":[23,55,93],"possible":[24],"scalar":[26],"linear":[27,123],"(damped":[30],"harmonic":[31],"oscillators":[32],"with":[33,76,105,113],"additive":[34,114],"noise),":[35],"where":[36],"statistics":[38],"are":[39],"Gaussian":[40,67],"and":[41,49,61,107],"can":[42],"be":[43],"calculated":[44],"exactly":[45],"in":[46],"continuous\u2010time":[48],"discrete\u2010time":[50],"cases.":[51],"matrix":[53,80],"equation":[54],"given":[56],"variances":[60],"correlation":[62],"using":[65],"one":[66],"random":[68],"variable":[69],"per":[70],"timestep.":[71],"The":[72],"only":[73],"Runge\u2013Kutta":[74],"method":[75],"a":[77],"nonsingular":[78],"tableau":[79],"gives":[82],"exact":[84],"steady":[85],"state":[86],"damping":[92],"implicit":[95,102],"midpoint":[96,103],"rule.":[97],"Numerical":[98],"experiments,":[99],"comparing":[100],"rule":[104],"Heun":[106],"leapfrog":[108],"on":[110],"nonlinear":[111],"or":[115],"multiplicative":[116],"noise,":[117],"produce":[118],"behavior":[119],"similar":[120],"to":[121],"case.":[124]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":13},{"year":2021,"cited_by_count":13},{"year":2020,"cited_by_count":12},{"year":2019,"cited_by_count":21},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":11},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":4}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
