{"id":"https://openalex.org/W2008382870","doi":"https://doi.org/10.1137/130932156","title":"Wiener Chaos Versus Stochastic Collocation Methods for Linear Advection-Diffusion-Reaction Equations with Multiplicative White Noise","display_name":"Wiener Chaos Versus Stochastic Collocation Methods for Linear Advection-Diffusion-Reaction Equations with Multiplicative White Noise","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2008382870","doi":"https://doi.org/10.1137/130932156","mag":"2008382870"},"language":"en","primary_location":{"id":"doi:10.1137/130932156","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130932156","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":"https://nottingham-repository.worktribe.com/output/1101315","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030093874","display_name":"Zhongqiang Zhang","orcid":"https://orcid.org/0000-0001-8032-7510"},"institutions":[{"id":"https://openalex.org/I107077323","display_name":"Worcester Polytechnic Institute","ror":"https://ror.org/05ejpqr48","country_code":"US","type":"education","lineage":["https://openalex.org/I107077323"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Zhongqiang Zhang","raw_affiliation_strings":["Worcester Polytechnic Institute"],"affiliations":[{"raw_affiliation_string":"Worcester Polytechnic Institute","institution_ids":["https://openalex.org/I107077323"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081243775","display_name":"M. V. Tretyakov","orcid":"https://orcid.org/0000-0002-7929-9046"},"institutions":[{"id":"https://openalex.org/I142263535","display_name":"University of Nottingham","ror":"https://ror.org/01ee9ar58","country_code":"GB","type":"education","lineage":["https://openalex.org/I142263535"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Michael V. Tretyakov","raw_affiliation_strings":["University of Nottingham"],"affiliations":[{"raw_affiliation_string":"University of Nottingham","institution_ids":["https://openalex.org/I142263535"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044537548","display_name":"B. L. Rozovski\u012d","orcid":null},"institutions":[{"id":"https://openalex.org/I175594653","display_name":"John Brown University","ror":"https://ror.org/02ct41q97","country_code":"US","type":"education","lineage":["https://openalex.org/I175594653"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Boris Rozovskii","raw_affiliation_strings":["Brown University"],"affiliations":[{"raw_affiliation_string":"Brown University","institution_ids":["https://openalex.org/I175594653"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009658255","display_name":"George Em Karniadakis","orcid":"https://orcid.org/0000-0002-9713-7120"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"George E. Karniadakis","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5030093874"],"corresponding_institution_ids":["https://openalex.org/I107077323"],"apc_list":null,"apc_paid":null,"fwci":2.5423,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.92165528,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"53","issue":"1","first_page":"153","last_page":"183"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9771000146865845,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13126","display_name":"Scientific Research and Discoveries","score":0.9706000089645386,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7985227108001709},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.7350911498069763},{"id":"https://openalex.org/keywords/multiplicative-noise","display_name":"Multiplicative noise","score":0.6133245229721069},{"id":"https://openalex.org/keywords/white-noise","display_name":"White noise","score":0.5809871554374695},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.48767054080963135},{"id":"https://openalex.org/keywords/polynomial-chaos","display_name":"Polynomial chaos","score":0.4602019488811493},{"id":"https://openalex.org/keywords/wiener-process","display_name":"Wiener process","score":0.4527566134929657},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44488152861595154},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.42793476581573486},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.4208020567893982},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.39660322666168213},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10961741209030151},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0777445137500763},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07512083649635315},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.06072387099266052}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7985227108001709},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.7350911498069763},{"id":"https://openalex.org/C18015164","wikidata":"https://www.wikidata.org/wiki/Q6935000","display_name":"Multiplicative noise","level":5,"score":0.6133245229721069},{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.5809871554374695},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.48767054080963135},{"id":"https://openalex.org/C197656079","wikidata":"https://www.wikidata.org/wiki/Q17147719","display_name":"Polynomial chaos","level":3,"score":0.4602019488811493},{"id":"https://openalex.org/C60391097","wikidata":"https://www.wikidata.org/wiki/Q1056809","display_name":"Wiener process","level":2,"score":0.4527566134929657},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44488152861595154},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.42793476581573486},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4208020567893982},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.39660322666168213},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10961741209030151},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0777445137500763},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07512083649635315},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.06072387099266052},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"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/C84462506","wikidata":"https://www.wikidata.org/wiki/Q173142","display_name":"Digital signal processing","level":2,"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/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/130932156","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130932156","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:10.1.1.700.5037","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.700.5037","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://users.wpi.edu/%7Ezzhang7/SINUM_WCEvsSCM.pdf","raw_type":"text"},{"id":"pmh:oai:nottingham-repository.worktribe.com:1101315","is_oa":true,"landing_page_url":"https://nottingham-repository.worktribe.com/output/1101315","pdf_url":null,"source":{"id":"https://openalex.org/S4306402483","display_name":"Repository@Nottingham (University of Nottingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142263535","host_organization_name":"University of Nottingham","host_organization_lineage":["https://openalex.org/I142263535"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"publishedVersion"}],"best_oa_location":{"id":"pmh:oai:nottingham-repository.worktribe.com:1101315","is_oa":true,"landing_page_url":"https://nottingham-repository.worktribe.com/output/1101315","pdf_url":null,"source":{"id":"https://openalex.org/S4306402483","display_name":"Repository@Nottingham (University of Nottingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142263535","host_organization_name":"University of Nottingham","host_organization_lineage":["https://openalex.org/I142263535"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"publishedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2248041640","display_name":null,"funder_award_id":"EP/K031430/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W87368160","https://openalex.org/W113954766","https://openalex.org/W657747163","https://openalex.org/W1542004730","https://openalex.org/W1580561995","https://openalex.org/W1587029759","https://openalex.org/W1945843680","https://openalex.org/W1977789473","https://openalex.org/W1982421072","https://openalex.org/W1983156129","https://openalex.org/W1986101505","https://openalex.org/W1987141392","https://openalex.org/W2004564211","https://openalex.org/W2008312770","https://openalex.org/W2014638237","https://openalex.org/W2022264564","https://openalex.org/W2032006621","https://openalex.org/W2041461479","https://openalex.org/W2056196028","https://openalex.org/W2057669046","https://openalex.org/W2057850781","https://openalex.org/W2083754610","https://openalex.org/W2087895654","https://openalex.org/W2109012275","https://openalex.org/W2119334003","https://openalex.org/W2140135904","https://openalex.org/W2143591652","https://openalex.org/W2144144515","https://openalex.org/W2178464435","https://openalex.org/W2317355914","https://openalex.org/W2322974491","https://openalex.org/W2332771484","https://openalex.org/W2506877196","https://openalex.org/W2799664482","https://openalex.org/W2949974907","https://openalex.org/W3021722416","https://openalex.org/W3100071526","https://openalex.org/W4238243565"],"related_works":["https://openalex.org/W2370840338","https://openalex.org/W2797263970","https://openalex.org/W2891782306","https://openalex.org/W2287391662","https://openalex.org/W339217817","https://openalex.org/W2125712855","https://openalex.org/W1989122168","https://openalex.org/W2044631309","https://openalex.org/W2054852670","https://openalex.org/W3111544124"],"abstract_inverted_index":{"We":[0,29],"compare":[1,37],"Wiener":[2,66,78],"chaos":[3,67],"and":[4,36],"stochastic":[5,48],"collocation":[6,49],"methods":[7,17,35,98],"for":[8,26,33,80,94],"linear":[9],"advection-reaction-diffusion":[10],"equations":[11,82],"with":[12,83,88],"multiplicative":[13],"white":[14],"noise.":[15],"Both":[16],"are":[18,99],"constructed":[19],"based":[20],"on":[21],"a":[22],"recursive":[23,46,64],"multistage":[24,47,65],"algorithm":[25],"long-time":[27],"integration.":[28],"derive":[30],"error":[31,91],"estimates":[32],"both":[34,97],"their":[38],"numerical":[39],"performance.":[40],"Numerical":[41],"results":[42],"confirm":[43],"that":[44],"the":[45,59,63,75,89,104],"method":[50,68],"is":[51,69,74],"of":[52,70,77,100],"order":[53,71,76,101],"$\\Delta$":[54],"(time":[55],"step":[56],"size)":[57],"in":[58,86,103],"second-order":[60,105],"moments":[61],"while":[62],"$\\Delta^{\\mathsf{N}}+\\Delta^2$":[72],"($\\mathsf{N}$":[73],"chaos)":[79],"advection-diffusion-reaction":[81],"commutative":[84],"noises,":[85,96],"agreement":[87],"theoretical":[90],"estimates.":[92],"However,":[93],"noncommutative":[95],"one":[102],"moments.":[106]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2015,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
