Lie group integrators with non-autonomous frozen vector fields

Lie group methods for non-autonomous semi-discretised in space, partial differential equations are considered. The use of time-dependent frozen vector fields and their corresponding algebra actions on a manifold is introduced. A new integration scheme, for the numerical solution of semi-linear problems, based on the so-called 'comutator-free Lie group methods', with algebra action arising from the prposed new framework is derived. The scheme is then compared with some existing methods in several numerical experiments.