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Numerical results confirm that the recursive multistage stochastic collocation method is of order $\\Delta$ (time step size) in the second-order moments while the recursive multistage Wiener chaos method is of order $\\Delta^{\\mathsf{N}}+\\Delta^2$ ($\\mathsf{N}$ is the order of Wiener chaos) for advection-diffusion-reaction equations with commutative noises, in agreement with the theoretical error estimates. However, for noncommutative noises, both methods are of order one in the second-order moments.<\/jats:p>","DOI":"10.1137\/130932156","type":"journal-article","created":{"date-parts":[[2015,1,8]],"date-time":"2015-01-08T09:23:49Z","timestamp":1420709029000},"page":"153-183","source":"Crossref","is-referenced-by-count":11,"title":["Wiener Chaos Versus Stochastic Collocation Methods for Linear  Advection-Diffusion-Reaction Equations with Multiplicative White Noise"],"prefix":"10.1137","volume":"53","author":[{"given":"Zhongqiang","family":"Zhang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael V.","family":"Tretyakov","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Boris","family":"Rozovskii","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"George E.","family":"Karniadakis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2015,1,8]]},"reference":[{"key":"atypb1","volume-title":"Stochastic Differential Equations: Theory and Applications","author":"Arnold L.","year":"1974"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1137\/050645142"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-15337-2_3"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1080\/17442509608834046"},{"key":"atypb5","first-page":"91","volume":"35","author":"Budhiraja A.","year":"1997","journal-title":"Appl. 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