Numerical integration of stochastic partial differential equations

Abstract

The solution of stochastic partial differential equations generally relies on numerical tools. However, conventional numerical procedures are not appropriate to solve such problems. In this paper an algorithm is proposed which allows the numerical treatment of a large class of stochastic partial differential equations. To this end we reduce stochastic partial differential equations to a system of stochastic ordinary differential equations which can be solved numerically by a well-known stochastic Euler-procedure. We apply our algorithm to two stochastic partial differential equations which are special examples because their stationary two-point correlation functions can be determined analytically. Our algorithm proves to work out very well when numerical results are compared with the analytic correlation function.