Numerical solution of ODEs

Seminar Scientific Computing - Summer Term 2011

Some general implicit processes for the numerical solution of ODEs

In an article from 1963 Rosenbrock shows one possibility to avoid the solution of non-linear systems for implicit Runge-Kutta methods. With the help of the article it was possible to create so-called Rosenbrock-Wanner methods which are quite popular today. These class of methods are linearly implicict Runge-Kutta methods. This means that the scheme contains a linearisation of the right-hand side of the ODE such that only linear systems has to be solved.

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