Extrapolation is a standard tool for improving the error of classical ODE methods. On the example of Magus methods we will demonstrate, how it can be used in the context of Lie group methods. The main difficulty with extrapolation are expensive operations exp and expinv (or commutator if we use the Baker-Campbell-Hausdorff formula). Numerical experiments obtained so far show, that the efficiency (the ratio between accuracy of the numerical solution and the number of arithmetical operations) of extrapolated Magnus methods is similar to the efficiency of the corresponding higher order Magnus method.

MINISIMPOSIUM SESSION: 12. Lie Group methods