A method for numerical approximation of a new class of fractional parabolic stochastic evolution equations is introduced and analysed. This class of equations has recently been proposed as a space-time extension of the SPDE-method in spatial statistics. A truncation of the spectral basis function expansion is used to discretise in space, and then a quadrature is used to approximate the temporal evolution of each basis coefficient. Strong error bounds are proved both for the spectral and temporal approximations. The method is tested and the results are verified by several numerical experiments.

翻译：本文提出并分析了一类新型分数阶抛物型随机演化方程的数值逼近方法。该类方程是空间统计学中SPDE方法在时空维度上的最新推广。我们采用谱基函数展开的截断实现空间离散，随后通过数值积分方法逼近各基函数系数的时间演化过程。文中严格证明了谱逼近与时间逼近的强误差界。通过多组数值实验对该方法进行了测试与验证。