Original article: Spectral collocation method for stochastic Burgers equation driven by additive noise

Authors:
Minoo Kamrani;S. Mohammad Hosseini
Affiliations:
Department of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, P.O. Box 14115-175, Tehran, Iran;Department of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, P.O. Box 14115-175, Tehran, Iran
Venue:
Mathematics and Computers in Simulation
Year:
2012

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Abstract

Almost nothing decisive has been said about collocation methods for solving SPDEs. Among the best of such SPDEs the Burgers equation shows a prototypical model for describing the interaction between the reaction mechanism, convection effect, and diffusion transport. This paper discusses spectral collocation method to reduce stochastic Burgers equation to a system of stochastic ordinary differential equations (SODEs). The resulting SODEs system is then solved by an explicit 3-stage stochastic Runge-Kutta method of strong order one. The convergence rate of Fourier collocation method for Burgers equation is also obtained. Some numerical experiments are included to show the performance of the method.