论文标题
分数指数集成器方案的强烈收敛，用于由标准和分数布朗运动驱动的时间分数SPDE的有限元离散化
Strong convergence of an fractional exponential integrator scheme for the finite element discretization of time-fractional SPDE driven by standard and fractional Brownian motions
论文作者
论文摘要
这项工作的目的是提供第一个强大的收敛性结果，这是一般时间级次级二阶二阶随机部分微分方程的数值近似值，涉及在（\ frac 12; 1）$ in（\ frac 12; 1）$的订单$α\ in（\ frac 12; 1）$中的caputo衍生物，并通过多重标准的棕色运动和添加的fb $ $ hurst $ $ $ h y y（frac 12; 1）$ hurs $ h y y \ y y \ y。对具有热记忆的培养基中颗粒传输的随机影响。我们证明存在和唯一性结果，并使用有限元元素和时间离散化进行空间离散化，并使用分数指数积分方案进行时间离散化。我们为我们的完全离散方案提供时间和空间收敛证明，结果表明，收敛顺序取决于初始数据的规律性，分数衍生物的功率和Hurst参数$ h $。
The aim of this work is to provide the first strong convergence result of numerical approximation of a general time-fractional second order stochastic partial differential equation involving a Caputo derivative in time of order $α\in(\frac 12; 1)$ and driven simultaneously by a multiplicative standard Brownian motion and additive fBm with Hurst parameter $H\in(\frac 12, 1)$, more realistic to model the random effects on transport of particles in medium with thermal memory. We prove the existence and uniqueness results and perform the spatial discretization using the finite element and the temporal discretization using a fractional exponential integrator scheme. We provide the temporal and spatial convergence proofs for our fully discrete scheme and the result shows that the convergence orders depend on the regularity of the initial data, the power of the fractional derivative, and the Hurst parameter $H$.
