Strong convergence in stochastic averaging principle for two time-scales stochastic partial differential equations

strong approximation for itô stochastic differential equations

in this paper, a class of semi-implicit two-stage stochastic runge-kutta methods (srks) of strong global order one, with minimum principal error constants are given. these methods are applied to solve itô stochastic differential equations (sdes) with a wiener process. the efficiency of this method with respect to explicit two-stage itô runge-kutta methods (irks), it method, milstien method, sem...

Numerical methods for stochastic partial differential equations with multiple scales

A new method for solving numerically stochastic partial differential equations (SPDEs) with multiple scales is presented. The method combines a spectral method with the heterogeneous multiscale method (HMM) presented in [W. E, D. Liu, and E. Vanden-Eijnden, Comm. Pure Appl. Math., 58(11):1544–1585, 2005]. The class of problems that we consider are SPDEs with quadratic nonlinearities that were s...

Numerical methods for stochastic partial differential equations with multiples scales

Article history: Received 23 May 2011 Received in revised form 3 October 2011 Accepted 27 November 2011 Available online 13 December 2011

Solving parabolic stochastic partial differential equations via averaging over characteristics

The method of characteristics (the averaging over the characteristic formula) and the weak-sense numerical integration of ordinary stochastic differential equations together with the Monte Carlo technique are used to propose numerical methods for linear stochastic partial differential equations (SPDEs). Their orders of convergence in the mean-square sense and in the sense of almost sure converg...

Stochastic Partial Differential Equations