On Wavelet-Galerkin Methods for Semilinear Parabolic Equations with Additive Noise
On Wavelet-Galerkin Methods for Semilinear Parabolic Equations with Additive Noise
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带加性噪声的半线性抛物型方程的小波-伽辽金方法
DOI：
10.1007/978-3-642-41095-6
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
K. Urban
中科院分区：
文献类型：
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作者：
M. Kovács;S. Larsson;K. Urban
我们考虑受加性噪声扰动的半线性随机热方程。通过欧拉方法进行时间离散后，方程被分为线性随机方程和非线性随机演化方程。采用非自适应小波伽辽金法对线性随机方程进行空间离散。首先求解该方程，并将其解代入非线性随机演化方程，采用自适应小波方法求解。我们提供总体误差的均方估计。
We consider the semilinear stochastic heat equation perturbed by additive noise. After time-discretization by Euler’s method the equation is split into a linear stochastic equation and a non-linear random evolution equation. The linear stochastic equation is discretized in space by a non-adaptive wavelet-Galerkin method. This equation is solved first and its solution is substituted into the nonlinear random evolution equation, which is solved by an adaptive wavelet method. We provide mean square estimates for the overall error.