Spectral Element Methods for Stochastic Differential Equations with Additive Noise

In this paper, we propose numerical schemes for stochastic differential equations driven by white noise and colored noise, respectively. For this purpose, we first discretize the white noise and colored noise, and give their regularity estimates. Then we use spectral element methods to solve the corresponding stochastic differential equations numerically. The approximation errors are derived, and the numerical results demonstrate high accuracy of the proposed schemes. AMS subject classifications: 65M70, 65L60, 41A10, 60H35