2002/01/01 by Dongbin Xiu, George Em Karniadakis · 2 citations
Decision Sciences · Physics and Astronomy · #Probabilistic and Robust Engineering Design #Scientific Research and Discoveries #Model Reduction and Neural Networks
paper · doi:10.1137/s1064827501387826
openalex publication_date 2002/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
Abstract. We present a new method for solving stochastic di®erential equations based on Galerkin projections and extensions of Wiener's polynomial chaos. Speci¯cally, we represent the stochastic processes with an optimum trial basis from the Askey family of orthogonal polynomials that reduces the dimensionality of the system and leads to exponential convergence of the error. Several continuous and discrete processes are treated, and numerical examples show substantial speed-up compared to Monte-Carlo simulations for low dimensional stochastic inputs.