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A detailed analysis of the accuracy of the PC representations, and of the different methods for nonpolynomial function evaluations, is performed. It is found that the integration method offers a robust and accurate approach for evaluating nonpolynomial functions, even when very high-order information is present in the PC expansions.<\/jats:p>","DOI":"10.1137\/s1064827503427741","type":"journal-article","created":{"date-parts":[[2005,1,10]],"date-time":"2005-01-10T21:00:25Z","timestamp":1105390825000},"page":"698-719","source":"Crossref","is-referenced-by-count":342,"title":["Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes"],"prefix":"10.1137","volume":"26","author":[{"given":"Bert J.","family":"Debusschere","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Habib N.","family":"Najm","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Philippe P.","family":"P\u00e9bay","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Omar M.","family":"Knio","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Roger G.","family":"Ghanem","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Olivier P.","family":"Le Ma\u0131\u2041tre","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,26]]},"reference":[{"key":"R1","unstructured":"Serial Fortran Solvers for ODE Initial Value Problems\n                      , http:\/\/www.llnl.gov\/CASC\/odepack\/ (2002)."},{"key":"R2","unstructured":"Slatec Common Mathematical Library, Version\n                      4.1, http:\/\/www.netlib.org\/slatec\/ (1993)."},{"key":"R3","doi-asserted-by":"crossref","unstructured":"G. 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