Cooper G J.
, Edinburgh, Scotland
FEBS Lett. 1969 Mar;2 Suppl 1:S22-S29. doi: 10.1016/0014-5793(69)80072-4.
This paper first discusses the conditions in which a set of differential equations should give stable solutions, starting with linear systems assuming that these do not differ greatly in this respect from non-linear systems. Methods of investigating the stability of particular systems are briefly discussed. Most real biochemical systems are known from observation to be stable, but little is known of the regions over which stability persists; moreover, models of biochemical systems may not be stable, because of inaccurate choice of parameter values.The separate problem of stability and accuracy in numerical methods of approximating the solution of systems of non-linear equations is then treated. Stress is laid on the consistently unsatisfactory results given by explicit methods for systems containing "stiff" equations, and implicit multistep methods are particularly recommended for this class of problem, which is likely to include many biochemical model systems. Finally, an iteration procedure likely to give convergence both in multistep methods and in the steady-state approach is recommended, and areas in which improvement in methods is likely to occur are outlined.
本文首先讨论一组微分方程应给出稳定解的条件，从线性系统开始，假设这些系统在这方面与非线性系统没有太大差异。简要讨论了研究特定系统稳定性的方法。从观察中可知，大多数实际生化系统是稳定的，但对于稳定性持续存在的区域却知之甚少；此外，由于参数值选择不准确，生化系统模型可能不稳定。接着讨论了在逼近非线性方程组解的数值方法中稳定性和准确性的单独问题。强调了对于包含“刚性”方程的系统，显式方法给出的结果一直不尽人意，对于这类可能包括许多生化模型系统的问题，特别推荐隐式多步法。最后，推荐了一种在多步法和稳态方法中都可能实现收敛的迭代过程，并概述了方法可能改进的领域。
