  Relaxation schemes for finding normal modes of nonlinear excitations are
described, and applied to the vortex-spinwave scattering problem in classical
two-dimensional easy-plane Heisenberg models. The schemes employ the square of
an effective Hamiltonian to ensure positive eigenvalues, together with an
evolution in time or a self-consistent Gauss-Seidel iteration producing
diffusive relaxation. We find some of the lowest frequency spinwave modes in a
circular system with a single vortex present. The method is used to describe
the vortex-spinwave scattering (S-matrix and phase shifts) and other dynamical
properties of vortices in ferromagnets and antiferromagnets, for systems larger
than that solvable by diagonalization methods. The lowest frequency modes
associated with translation of the vortex center are used to estimate the
vortex mass.
