Lie group integrators with non-autonomous frozen vector fields

Lie group methods for nonautonomous semi-discretized in space, partial differential equations are considered. The choice of frozen vector field and its corresponding algebra action on the manifold for such problems is discussed. A new exponential integrator for semilinear problems based on commutator free Lie group methods with algebra action arising from the solutions of differential equations with nonautonomous frozen vector fields is derived. The proposed new scheme is then compared with some existing methods in several numerical experiments.