The Wiener–Askey polynomial chaos for stochastic differential equations. (English) Zbl 1014.65004

Xiu, Dongbin; Karniadakis, George Em

SIAM J. Sci. Comput. 24, No. 2, 619-644 (2002).

MSC:

65C30	Numerical solutions to stochastic differential and integral equations
65C05	Monte Carlo methods
60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)
34F05	Ordinary differential equations and systems with randomness
60H35	Computational methods for stochastic equations (aspects of stochastic analysis)

Keywords:

polynomial chaos; Askey scheme; orthogonal polynomials; stochastic differential equations; spectral methods; Galerkin projection; exponential convergence; numerical examples; Monte Carlo simulations