论文标题
由粗噪声驱动的随机非线性分数扩散方程的数值近似
Numerical Approximation for Stochastic Nonlinear Fractional Diffusion Equation Driven by Rough Noise
论文作者
论文摘要
在这项工作中，我们有兴趣建立由分数布朗纸驱动的随机分数扩散方程的完全离散的方案，布朗尼纸在时间和空间上具有hurst参数$ h_ {1}，h_ {2} \ in（in（0，\ frac {1}} {2} {2} {2} {2} {2}] $。粗糙的噪声并讨论了接近的接收，有限的元素和后退卷积正交方法用于离散空间和临时算子的正则方程，并开发了一些数值示例。
In this work, we are interested in building the fully discrete scheme for stochastic fractional diffusion equation driven by fractional Brownian sheet which is temporally and spatially fractional with Hurst parameters $H_{1}, H_{2} \in(0,\frac{1}{2}]$. We first provide the regularity of the solution. Then we employ the Wong-Zakai approximation to regularize the rough noise and discuss the convergence of the approximation. Next, the finite element and backward Euler convolution quadrature methods are used to discretize spatial and temporal operators for the obtained regularized equation, and the detailed error analyses are developed. Finally, some numerical examples are presented to confirm the theory.
