A high-accuracy time discretization is discussed to numerically solve the nonlinear fractional diffusion equation forced by a space-time white noise. The main purpose of this paper is to improve the temporal convergence rate by modifying the semi-implicit Euler scheme. The solution of the equation is only H\"older continuous in time, which is disadvantageous to improve the temporal convergence rate. Firstly, the system is transformed into an equivalent form having better regularity than the original one in time. But the regularity of nonlinear term remains unchanged. Then, combining Lagrange mean value theorem and independent increments of Brownian motion leads to a higher accuracy discretization of nonlinear term which ensures the implementation of the proposed time discretization scheme without loss of convergence rate. Our scheme can improve the convergence rate from ${\min\{\frac{\gamma}{2\alpha},\frac{1}{2}\}}$ to ${\min\{\frac{\gamma}{\alpha},1\}}$ in the sense of mean-squared $L^2$-norm. The theoretical error estimates are confirmed by extensive numerical experiments.

翻译：讨论高精确度时间分解, 以便用数字方式解决由时空白噪音强制形成的非线性分散扩散方程式。 本文的主要目的是通过修改半隐含电极方案来提高时间趋同率。 等式的解决方案只是H\"老的连续时间, 这不利于提高时间趋同率。 首先, 系统转换成一种等同的形式, 其规律性比原先的要好。 但非线性术语的规律性保持不变 。 然后, 将布朗运动的拉格兰特平均值理论值和独立递增值结合起来, 导致非线性术语的更精确分解率, 以确保实施拟议的时间分解计划, 而不丧失趋同率 。 我们的计划可以通过广泛的数字实验来证实理论错误估计。