Implementation of Rosenbrock Methods
Implementation of Rosenbrock Methods
复制标题
Rosenbrock 方法的实施
DOI：
10.1145/355993.355994
复制
发表时间：
1982
期刊：
影响因子：
--
通讯作者：
L. Shampine
中科院分区：
文献类型：
--
作者：
L. Shampine
Rosenbrock 公式在解决常微分方程 (ODE) 刚性系统的初值问题的研究代码中显示出良好的前景。为了帮助评估其实用价值，作者根据这样的公式编写了一个数学软件。这需要各种算法和软件开发。本文报告了普遍感兴趣的内容。其中一种方法是在每一步根据问题的刚度自动选择显式龙格-库塔公式或罗森布罗克公式。求解线性系统对于刚性 ODE 方法很重要，并且对于 Rosenbrock 方法来说相当特殊。得出了对线性系统状况的廉价、有效的估计。一些数值结果被提出来说明进展。
Rosenbrock formulas have shown promise in research codes for the solution of initial-value problems for stiff systems of ordinary differential equations (ODEs). To help assess their practical value, the author wrote an item of mathematical software based on such a formula. This required a variety of algorithmic and software developments. Those of general interest are reported in this paper. Among them is a way to select automatically, at every step, an explicit Runge-Kutta formula or a Rosenbrock formula according to the stiffness of the problem. Solving linear systems is important to methods for stiff ODEs, and is rather special for Rosenbrock methods. A cheap, effective estimate of the condition of the linear systems is derived. Some numerical results are presented to illustrate the developments.