The simulation of chemical kinetics involving multiple scales constitutes a modeling challenge (from ordinary differential equations to Markov chain) and a computational challenge (multiple scales, large dynamical systems, time step restrictions). In this paper we propose a new discrete stochastic simulation algorithm: the postprocessed second kind stabilized orthogonal $\tau$-leap Runge-Kutta method (PSK-$\tau$-ROCK). In the context of chemical kinetics this method can be seen as a stabilization of Gillespie's explicit $\tau$-leap combined with a postprocessor. The stabilized procedure allows to simulate problems with multiple scales (stiff), while the postprocessing procedure allows to approximate the invariant measure (e.g. mean and variance) of ergodic stochastic dynamical systems. We prove stability and accuracy of the PSK-$\tau$-ROCK. Numerical experiments illustrate the high reliability and efficiency of the scheme when compared to other $\tau$-leap methods.

中文翻译：

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用于模拟化学动力学的最优显式稳定后处理 $τ$-leap 方法

涉及多尺度的化学动力学模拟构成了建模挑战（从常微分方程到马尔可夫链）和计算挑战（多尺度、大型动力系统、时间步长限制）。在本文中，我们提出了一种新的离散随机模拟算法：后处理第二类稳定正交$\tau$-leap Runge-Kutta方法（PSK-$\tau$-ROCK）。在化学动力学的背景下，这种方法可以看作是 Gillespie 的显式 $\tau$-leap 与后处理器相结合的稳定化。稳定程序允许模拟具有多个尺度（僵硬）的问题，而后处理程序允许近似遍历随机动力系统的不变度量（例如均值和方差）。我们证明了 PSK-$\tau$-ROCK 的稳定性和准确性。