In this paper, we consider the numerical approximation of stochastic partial differential equations driven by infinite dimensional fractional Brownian motion with Hurst index $H>\frac{1}{2}$. A Fourier spectral collocation approximation is used in space and semi-implicit Euler method is applied for the temporal approximation. Our aim is to investigate the convergence of the proposed method. Optimal strong convergence error estimates in mean-square sense are derived and numerical experiments are presented and confirm theoretical results.

中文翻译：

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分数布朗运动的随机偏微分方程的谱配置方法

在本文中，我们考虑由具有Hurst指数的无穷维分数布朗运动驱动的随机偏微分方程的数值逼近 $H>\frac{\mathrm{1个}}{2}$。在空间中使用傅立叶频谱配置近似，并且在时间近似中使用半隐式欧拉方法。我们的目的是研究所提出方法的收敛性。推导了均方意义上的最优强收敛误差估计，并进行了数值实验并证实了理论结果。