Spectral collocation method for stochastic Burgers equation driven by additive noise
Almost nothing decisive has been said about collocation methods for solving SPDEs. Among the best of such SPDEs the Burgers equation presents a prototypical model for describing the interaction between reaction mechanism, convection effect and diffusion transport. This paper discusses the spectral collocation method to reduce the stochastic Burgers equation to a system of stochastic ordinary differential equations (SODEs). The resulting SODEs system is then solved by an explicit three-stage stochastic Runge-Kutta method of strong order one. The convergence rate of the Fourier collocation method for Burgers equation is also obtained. Some numerical experiments are included to illustrate the performance of the method.
stochastic ordinary differential equation
stochastic partial differential equation
scientific article; zbMATH DE number 6107055
scientific article