Wiener Chaos Expansion and Numerical Solutions of Stochastic PDE by Wuan Luo

Wiener Chaos Expansion and Numerical Solutions of Stochastic PDE by Wuan Luo

Stochastic partial differential equations (PDE) are widely used in modeling complex phenomena of fluid dynamics, random media, materials science, chemistry, biology, etc, where large structures and dominant dynamics are governed by deterministic laws, while the unresolved small scales, microscopic effects, and other uncertainties can be naturally modeled by stochastic processes. This book studies how to solve stochastic PDEs numerically based on Wiener chaos (Hermite polynomial chaos) expansion. Wiener chaos expansion is a spectral expansion of the stochastic solution in the probability space. The coefficients of the expansion are governed by a coupled deterministic PDE system, which represents the propagation of the space time randomness inherent to the original stochastic PDE. This book provides a detailed and rigorous introduction to the Wiener chaos expansion theory, and addresses a few critical difficulties of its numerical solutions for stochastic PDEs. Some interesting numerical applications are also provided, such as invariant measure of stochastic Burger equations, front propagation of stochastic reaction-diffusion equations, etc.

SKU	Unavailable
ISBN 13	9783639174267
ISBN 10	3639174267
Title	Wiener Chaos Expansion and Numerical Solutions of Stochastic PDE
Author	Wuan Luo
Condition	Unavailable
Binding Type	Paperback
Publisher	VDM Verlag
Year published	2010-05-26
Number of pages	216
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
Note	Unavailable