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Method of lines for stochastic boundary-value problems with additive noise. (English) Zbl 1142.65007
Summary: We propose a new numerical method for solving stochastic boundary-value problems. The method uses the deterministic method of lines to treat the time, space and randomness separately. The emphasis in the present study is given to stochastic partial differential equations with forced additive noise. The spatial discretization is carried out using a second-order finite volume method, while the associated stochastic differential system is numerically solved using a class of stochastic Runge-Kutta methods. The performance of the proposed methods is tested for a stochastic advection-diffusion problem and a stochastic Burgers equation driven with white noise. Numerical results are presented in both one and two space dimensions.

MSC:
65C30 Numerical solutions to stochastic differential and integral equations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
35R60 PDEs with randomness, stochastic partial differential equations
35Q53 KdV equations (Korteweg-de Vries equations)
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
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