Abstract We consider the strong convergence of the numerical methods for solving stochastic subdiffusion problem driven by an integrated space-time white noise. The time fractional derivative is approximated by using the L1 scheme and the time fractional integral is approximated with the Lubich's first order convolution quadrature formula. We use the Euler method to approximate the noise in time and use the truncated series to approximate the noise in space. The spatial variable is discretized by using the linear finite element method. Applying the idea in Gunzburger et al. (2019) [14] , we express the approximate solutions of the fully discrete scheme by the convolution of the piecewise constant function and the inverse Laplace transform of the resolvent related function. Based on such convolution expressions of the approximate solutions, we obtain the optimal convergence orders of the fully discrete scheme in spatial multi-dimensional cases by using the Laplace transform method and the corresponding resolvent estimates.

中文翻译：

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集成时空白噪声驱动的随机子扩散问题的L1方案分析

摘要 我们考虑了求解由集成时空白噪声驱动的随机子扩散问题的数值方法的强收敛性。时间分数阶导数用L1方案近似，时间分数积分用Lubich的一阶卷积求积公式近似。我们使用欧拉方法在时间上近似噪声，并使用截断级数来近似空间上的噪声。空间变量采用线性有限元方法离散化。在 Gunzburger 等人中应用这个想法。(2019) [14] ，我们通过分段常数函数的卷积和求解相关函数的拉普拉斯逆变换来表达完全离散方案的近似解。基于这种近似解的卷积表达式，