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.