For ODEs which contain stiff and non-stiff parts often so-called partioned Runge-Kutta methods are used, i.e. the non-stiff part is integrated with the help of an explicit Runge-Kutta-method, the stiff part with an implicit Runge-Kutta scheme. For such schemes an automatic stiffness detection is important. As for usual Runge-Kutta schemes automatic stepsize selection can be implemented with the help of embedding.
Previous knowledge: Introduction into Scientific Computing