Numerical studies of the stochastic Korteweg-de Vries equation

Authors:
Guang Lin;Leopold Grinberg;George Em Karniadakis
Affiliations:
Division of Applied Mathematics, Brown University, 182 George Street, Box F, Providence, RI 02912, USA;Division of Applied Mathematics, Brown University, 182 George Street, Box F, Providence, RI 02912, USA;Division of Applied Mathematics, Brown University, 182 George Street, Box F, Providence, RI 02912, USA
Venue:
Journal of Computational Physics
Year:
2006

Citing 3
Cited 1

Numerical simulation of the stochastic Korteweg-de Vries equation

Physica D
A Local Discontinuous Galerkin Method for KdV Type Equations

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Abstract

We present numerical solutions of the stochastic Korteweg-de Vries equation for three cases corresponding to additive time-dependent noise, multiplicative space-dependent noise and a combination of the two. We employ polynomial chaos for discretization in random space, and discontinuous Galerkin and finite difference for discretization in physical space. The accuracy of the stochastic solutions is investigated by comparing the first two moments against analytical and Monte Carlo simulation results. Of particular interest is the interplay of spatial discretization error with the stochastic approximation error, which is examined for different orders of spatial and stochastic approximation.