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Title: Numerical approximation of nonlinear SPDE’s

The numerical analysis of stochastic parabolic partial differential equations of the form$$\begin{aligned} du + A(u)\, dt = f \,dt + g \, dW, \end{aligned}$$du+A(u)dt=fdt+gdW,is surveyed, whereAis a nonlinear partial operator andWa Brownian motion. This manuscript unifies much of the theory developed over the last decade into a cohesive framework which integrates techniques for the approximation of deterministic partial differential equations with methods for the approximation of stochastic ordinary differential equations. The manuscript is intended to be accessible to audiences versed in either of these disciplines, and examples are presented to illustrate the applicability of the theory.

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Stochastics and Partial Differential Equations: Analysis and Computations
Springer Science + Business Media
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National Science Foundation
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