Rosenbrock-Type Methods
Rosenbrock-Type Methods
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Rosenbrock 型方法
DOI：
10.1007/978-3-642-05221-7_7
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
G. Wanner
中科院分区：
文献类型：
--
作者：
E. Hairer;G. Wanner
...本节讨论。在已经对刚性方程给出满意结果的方法中，Rosenbrock 方法是最容易编程的。我们将在本节中描述他们的理论，这将引导我们找到第一个“僵化”代码。 Rosenbrock 方法属于一大类试图避免非线性系统并用一系列线性系统代替的方法。因此，我们将这些方法称为线性隐式龙格-库塔方法。在文献中，此类方法通常被称为“半隐式”（或者是“半显式”？），或“广义”或“修改”或“自适应”或“加性”龙格-库塔方法。
... is discussed in this section. Among the methods which already give satisfactory results for stiff equations, Rosenbrock methods are the easiest to program. We shall describe their theory in this section, which will lead us to our first “stiff” code. Rosenbrock methods belong to a large class of methods which try to avoid nonlinear systems and replace them by a sequence of linear systems. We therefore call these methodslinearly implicit Runge-Kutta methods. In the literature such methods are often called “semi-implicit” (or was it “semi-explicit”?), or “generalized” or “modified” or “adaptive” or “additive” Runge-Kutta methods.