Computational methods for some stochastic partial differential equations

Many physical systems are naturally modeled by partial differential equations. Often these systems have perturbations or other uncertainties that can be effectively modeled by additive white Gaussian noise. These stochastic models are usually called stochastic partial differential equations (SPDE's). To use these models effectively in applications it is important to investigate numerical methods for solving SPDE's. It seems that there has been a very limited amount of work on these numerical questions (e.g. [1,3]). For the computational methods for the stochastic partial differential equations some well known finite difference methods are used to determine which ones perform well for some families of stochastic partial differential equations. These methods include the explicit, fully implicit, and the Crank-Nicolson methods. The methods are compared for different mesh sizes in time and space and for different intensities of the noise.