  Here we present a new particle-mesh galactic N-body code that uses the full
multigrid algorithm for solving the modified Poisson equation of the Quasi
Linear formulation of Modified Newtonian Dynamics (QUMOND). A novel approach
for handling the boundary conditions using a refinement strategy is implemented
and the accuracy of the code is compared with analytical solutions of Kuzmin
disks. We then employ the code to compute the predicted rotation curves for a
sample of five spiral galaxies from the THINGS sample. We generated static
N-body realisations of the galaxies according to their stellar and gaseous
surface densities and allowed their distances, mass-to-light ratios (M/L) and
both the stellar and gas scale-heights to vary in order to estimate the best
fit parameters. We found that NGC 3621, NGC 3521 and DDO 154 are well fit by
MOND using expected values of the distance and M/L. NGC 2403 required a
moderately larger $M/L$ than expected and NGC 2903 required a substantially
larger value. The surprising result was that the scale-height of the dominant
baryonic component was well constrained by the rotation curves: the gas
scale-height for DDO 154 and the stellar scale-height for the others. In fact,
if the suggested stellar scale-height (one-fifth the stellar scale-length) was
used in the case of NGC 3621 and NGC 3521 it would not be possible to produce a
good fit to the inner rotation curve. For each of the four stellar dominated
galaxies, we calculated the vertical velocity dispersions which we found to be,
on the whole, quite typical compared with observed stellar vertical velocity
dispersions of face on spirals. We conclude that modelling the gas
scale-heights of the gas rich dwarf spiral galaxies will be vital in order to
make precise conclusions about MOND.
