Rational Runge-Kutta methods are not suitable for stiff systems of ODEs

摘要

The present paper shows that rational RK-methods are not very appropriate to solve stiff differential equations. The CA0-stability (i.e. componentwise contractivity) is defined and the non-existence of CA0-stable rational RK-methods is demonstrated. Furthermore it is shown that the stepsizes which can be expected when solving a stiff differential system with a rational or with an explicit linear RK-method are of the same order of magnitude.