Strong convergence rates of an explicit scheme for stochastic Cahn-Hilliard equation with additive noise
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In this paper, we propose and analyze an explicit time-stepping scheme for a spatial discretization of stochastic Cahn-Hilliard equation with additive noise. The fully discrete approximation combines a spectral Galerkin method in space with a tamed exponential Euler method in time. In contrast to implicit schemes in the literature, the explicit scheme here is easily implementable and produces significant improvement in the computational efficiency. It is shown that the fully discrete approximation converges strongly to the exact solution, with strong convergence rates identified. To the best of our knowledge, it is the first result concerning an explicit scheme for the stochastic Cahn-Hilliard equation. Numerical experiments are finally performed to confirm the theoretical results.
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