Advanced Stiff Systems Detection

The paper deals with stiff systems of differential equations. To solve this sort of system numerically is a difficult task. There are many (implicit) methods for solving stiff systems of ordinary differential equations (ODE's), from the most simple such as implicit Euler method to more sophisticated (implicit Runge-Kutta methods) and finally the general linear methods. The mathematical formulation of the methods often looks clear, however the implicit nature of those methods implies several implementation problems. Usually a quite complicated auxiliary system of equations has to be solved in each step. These facts lead to immense amount of work to be done in each step of the computation. These are the reasons why one has to think twice before using the stiff solver and to decide between the stiff and non-stiff solver.