  We present a detailed description of the methods used in our model of mode
instability in high-power, rare earth-doped, large-mode-area fiber amplifiers.
Our model assumes steady-periodic behavior, so it is appropriate to operation
after turn on transients have dissipated. It can be adapted to transient cases
as well. We describe our algorithm, which includes propagation of the signal
field by fast-Fourier transforms, steady-state solutions of the laser gain
equations, and two methods of solving the time-dependent heat equation:
alternating-direction-implicit integration, and the Green's function method for
steady-periodic heating.
