Spectral Element Methods for Stochastic Differential Equations with Additive Noise (Journal of Mathematical Study, 2019)
In this paper, we propose numerical schemes for stochastic differential equationsdriven by white noise and colored noise, respectively. For this purpose, we firstdiscretize the white noise and colored noise, and give their regularity estimates. Thenwe use spectral element methods to solve the corresponding stochastic differentialequations numerically. The approximation errors are derived, and the numerical resultsdemonstrate high accuracy of the proposed schemes.
Keywords: Stochastic differential equations; spectral element methods; high accuracy.