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Barycentric interpolation of interface solution for solving stochastic partial differential equations on non-overlapping subdomains with additive multi-noises. (English) Zbl 1390.35165

Summary: The purpose of this paper is to develop a new numerical method for solving a class of stochastic partial differential equations with additive multi-noise. Based on the domain decomposition method, we combine the deterministic method of lines and the stochastic Itô-Taylor method to construct high-order stochastic numerical method. For numerical approximation of the interface solutions, we introduce the Barycentric interpolation method. The solution is then carried out by collecting the interior solutions on the subdomains and the updated interface solutions. Finally, we computationally analyse on meaningful subdomains with linear and nonlinear interfaces, the case of a stochastic advection-diffusion with additive multi-noise and Dirichlet boundary conditions.

MSC:

35K57 Reaction-diffusion equations
35R60 PDEs with randomness, stochastic partial differential equations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
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