Higher Order Strong Approximations of Semilinear Stochastic Wave Equation with Additive Space-time White Noise
Higher Order Strong Approximations of Semilinear Stochastic Wave Equation with Additive Space-time White Noise
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DOI：
10.1137/130937524
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发表时间：
2013-08
期刊：
影响因子：
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通讯作者：
Xiaojie Wang;S. Gan;Jingtian Tang
中科院分区：
文献类型：
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作者：
Xiaojie Wang;S. Gan;Jingtian Tang
开发了新型全离散格式来数值逼近加性时空白色噪声驱动的半线性随机波动方程。空间离散采用谱Galerkin方法，时间近似采用包含噪声线性泛函的指数时间积分器。所得到的完全离散的计划是非常容易实现的，并允许更高的强收敛速度比现有的时间步进计划，如Crank-Nicolson-Maruyama计划和随机三角法。特别是，它表明，新的计划实现的时间顺序为1- \n $任意小的$\n>0$，这超过了障碍秩序的沃尔什$\frac{1}{2}$。数值结果证实了新格式具有更高的收敛速度和计算效率。
Novel fully discrete schemes are developed to numerically approximate a semilinear stochastic wave equation driven by additive space-time white noise. Spectral Galerkin method is proposed for the spatial discretization, and exponential time integrators involving linear functionals of the noise are introduced for the temporal approximation. The resulting fully discrete schemes are very easy to implement and allow for higher strong convergence rate in time than existing time-stepping schemes such as the Crank-Nicolson-Maruyama scheme and the stochastic trigonometric method. Particularly, it is shown that the new schemes achieve in time an order of $1- \epsilon$ for arbitrarily small $\epsilon >0$, which exceeds the barrier order $\frac{1}{2}$ established by Walsh. Numerical results confirm higher convergence rates and computational efficiency of the new schemes.