Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 24, Issue 2, Pages 619-644Publisher
SIAM PUBLICATIONS
DOI: 10.1137/S1064827501387826
Keywords
polynomial chaos; Askey scheme; orthogonal polynomials; stochastic differential equations; spectral methods; Galerkin projection
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We present a new method for solving stochastic differential equations based on Galerkin projections and extensions of Wiener's polynomial chaos. Specifically, 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.
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