Fischer T H, White G C
Center for Thrombosis and Hemostasis, Department of Medicine, University of North Carolina, Chapel Hill 27599.
Comput Appl Biosci. 1990 Jul;6(3):173-7. doi: 10.1093/bioinformatics/6.3.173.
A numerical method for evaluating chemical rate equations is presented. This method was developed by expressing the system of coupled, first-degree, ordinary differential chemical rate equations as a single tensor equation. The tensorial rate equation is invariant in form for all reversible and irreversible reaction schemes that can be expressed as first- and second-order reaction steps, and can accommodate any number of reactive components. The tensor rate equation was manipulated to obtain a simple formula (in terms of rate constants and initial concentrations) for the power coefficients of the Taylor expansion of the chemical rate equation. The Taylor expansion formula was used to develop a FORTRAN algorithm for analysing the time development of chemical systems. A computational experiment was performed with a Michaelis-Menten scheme in which step size and expansion order (to the 100th term) were varied; the inclusion of high-order terms of the Taylor expansion was shown to reduce truncation and round-off errors associated with Runge-Kutta methods and lead to increased computational efficiency.
提出了一种评估化学速率方程的数值方法。该方法是通过将耦合的一阶常微分化学速率方程组表示为单个张量方程而开发的。对于所有可表示为一阶和二阶反应步骤的可逆和不可逆反应方案，张量速率方程在形式上是不变的，并且可以容纳任意数量的反应组分。对张量速率方程进行处理，以获得化学速率方程泰勒展开式幂系数的简单公式（根据速率常数和初始浓度）。利用泰勒展开式公式开发了一种用于分析化学系统时间演化的FORTRAN算法。对米氏方案进行了计算实验，其中步长和展开阶数（到第100项）是变化的；结果表明，包含泰勒展开式的高阶项可减少与龙格 - 库塔方法相关的截断和舍入误差，并提高计算效率。
