Numerical solution of the Burgers equation with Neumann boundary noise

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In this paper we investigate the numerical solution of the one-dimensional Burgers equation with Neumann boundary noise. For the discretization scheme we use the Galerkin approximation in space and the exponential Euler method in time. The impact of the boundary noise on the solution is discussed in several numerical examples. Moreover, we analyze and illustrate some properties of the stochastic term and study the convergence numerically.

论文关键词:60H15,60H35,65C05,65C30,60H10,Burgers equation,Boundary Neumann noise,Galerkin method,Weak approximation,Exponential Euler scheme,Impact of noise

论文评审过程:Received 7 October 2015, Revised 5 July 2016, Available online 22 July 2016, Version of Record 5 August 2016.

论文官网地址:https://doi.org/10.1016/j.cam.2016.07.005