论文标题
Fitzhugh的分裂方案 - Nagumo随机部分微分方程
Splitting schemes for FitzHugh--Nagumo stochastic partial differential equations
论文作者
论文摘要
我们设计和研究拆分集成剂，用于随机Fitzhugh-Nagumo系统的时间离散化。该系统是在神经细胞中信号传播的模型，其中电压变量是溶液的一维抛物线PDE解决方案，该抛物线PDE具有由加性时空白噪声驱动的立方非线性。我们首先表明数值解决方案有有限的时刻。然后，我们证明了分裂方案至少具有强大的收敛速度$ 1/4 $。最后，提供了说明分裂方案性能的数值实验。
We design and study splitting integrators for the temporal discretization of the stochastic FitzHugh--Nagumo system. This system is a model for signal propagation in nerve cells where the voltage variable is solution of a one-dimensional parabolic PDE with a cubic nonlinearity driven by additive space-time white noise. We first show that the numerical solutions have finite moments. We then prove that the splitting schemes have, at least, the strong rate of convergence $1/4$. Finally, numerical experiments illustrating the performance of the splitting schemes are provided.
