Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, Maryland 21250, USA.
J Chem Phys. 2011 Jan 28;134(4):044129. doi: 10.1063/1.3532768.
Tau leaping methods enable efficient simulation of discrete stochastic chemical systems. Stiff stochastic systems are particularly challenging since implicit methods, which are good for stiffness, result in noninteger states. The occurrence of negative states is also a common problem in tau leaping. In this paper, we introduce the implicit Minkowski-Weyl tau (IMW-τ) methods. Two updating schemes of the IMW-τ methods are presented: implicit Minkowski-Weyl sequential (IMW-S) and implicit Minkowski-Weyl parallel (IMW-P). The main desirable feature of these methods is that they are designed for stiff stochastic systems with molecular copy numbers ranging from small to large and that they produce integer states without rounding. This is accomplished by the use of a split step where the first part is implicit and computes the mean update while the second part is explicit and generates a random update with the mean computed in the first part. We illustrate the IMW-S and IMW-P methods by some numerical examples, and compare them with existing tau methods. For most cases, the IMW-S and IMW-P methods perform favorably.
tau 跃方法能够有效地模拟离散随机化学系统。刚性随机系统特别具有挑战性，因为对于刚度很好的隐式方法，会导致非整数状态。在 tau 跃中，负状态的出现也是一个常见问题。在本文中，我们引入了隐式 Minkowski-Weyl tau（IMW-τ）方法。提出了两种 IMW-τ方法的更新方案：隐式 Minkowski-Weyl 顺序（IMW-S）和隐式 Minkowski-Weyl 并行（IMW-P）。这些方法的主要特点是，它们专为分子拷贝数从小到大的刚性随机系统设计，并且不会舍入产生整数状态。这是通过使用分步方法实现的，其中第一部分是隐式的，计算平均值更新，而第二部分是显式的，使用第一部分计算的平均值生成随机更新。我们通过一些数值示例说明了 IMW-S 和 IMW-P 方法，并将它们与现有的 tau 方法进行了比较。对于大多数情况，IMW-S 和 IMW-P 方法表现良好。
