| Abstract: |
| In this talk, we propose and analyze energy-preserving numerical schemes for the stochastic nonlinear wave equation.These numerical schemes, called stochastic scalar auxiliary variable (SAV) schemes, are constructed by transforming the considered equation into a higher dimensional stochastic system with a stochastic SAV. We prove that they can be solved explicitly, and preserve the modiified energy evolution law and the regularity structure of the original system. These structure-preserving properties are the keys to overcoming the mutual effect of noise and nonlinearity. By providing new regularity estimates of the introduced SAV, we obtain the strong convergence rate of stochastic SAV schemes under Lipschitz conditions. Furthermore, based on the modified energy evolution laws, we derive the exponential moment bounds and sharp strong convergence rate of the proposed schemes for equation with a non-globally Lipschitz nonlinearity in the additive noise case. To the best of our knowledge, this is the first result on the construction and strong convergence of semi-implicit energy-preserving schemes for stochastic nonlinear wave equations. |
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