Maclachlan Mary C, Sundnes Joakim, Spiteri Raymond J
Simula Research Laboratory, Lysaker, Norway.
Comput Methods Biomech Biomed Engin. 2007 Oct;10(5):317-26. doi: 10.1080/10255840701259301.
Mathematical models for the electrical activity in cardiac cells are normally formulated as systems of ordinary differential equations (ODEs). The equations are nonlinear and describe processes occurring on a wide range of time scales. Under normal accuracy requirements, this makes the systems stiff and therefore challenging to solve numerically. As standard implicit solvers are difficult to implement, explicit solvers such as the forward Euler method are commonly used, despite their poor efficiency. Non-standard formulations of the forward Euler method, derived from the analytical solution of linear ODEs, can give significantly improved performance while maintaining simplicity of implementation. In this paper we study the performance of three non-standard methods on two different cell models with comparable complexity but very different stiffness characteristics.
心脏细胞电活动的数学模型通常被表述为常微分方程（ODEs）系统。这些方程是非线性的，描述了在广泛时间尺度上发生的过程。在正常精度要求下，这使得系统具有刚性，因此在数值求解时具有挑战性。由于标准隐式求解器难以实现，尽管效率低下，但诸如前向欧拉方法之类的显式求解器仍被普遍使用。从线性ODEs的解析解推导而来的前向欧拉方法的非标准公式，在保持实现简单性的同时，可以显著提高性能。在本文中，我们研究了三种非标准方法在两个具有可比复杂性但刚度特性非常不同的不同细胞模型上的性能。
