  Stiff and chaotic differential equations are challenging for time-stepping
numerical methods. For explicit methods, the required time step resolution
significantly exceeds the resolution associated with the smoothness of the
exact solution for specified accuracy. In order to improve efficiency, the
question arises whether transformation to asymptotically stable solutions can
be performed, for which neighbouring solutions converge towards each other at a
controlled rate. Employing the concept of local Lyapunov exponents, it is
demonstrated that chaotic differential equations can be successfully
transformed to obtain high accuracy, whereas stiff equations cannot. For
instance, the accuracy of explicit fourth order Runge-Kutta solution of the
Lorenz chaotic equations can be increased by two orders of magnitude.
Alternatively, the time step can be significantly extended with retained
accuracy.
