  We test the scaling behaviour of Wilson, hypercube, maximally twisted mass
and overlap fermion actions in dynamical simulations of the 2-dimensional
massive Schwinger model. We also present possibilities to simulate overlap
fermions dynamically by replacing the exact overlap operator by an approximate
version. This approximation is used either as only the guidance Hamiltonian,
keeping the exact overlap operator as the accept/reject Hamiltonian or for
both, the guidance and accept/reject Hamiltonian in the Hybrid Monte Carlo
algorithm. In the latter case we test whether the approximation error can be
corrected for by computing the determinant ratio of the exact and the
approximate overlap operators stochastically.
