Numerical approximation of nonlinear SPDE’s

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