  Using a cell dynamic system (CDS) simulation scheme, we investigate the
phase-ordering dynamics of non-conserved O(n) models without topological
defects, i.e. for $n > d+1$ where $d$ is the spatial dimensionality. In
particular, we consider zero-temperature quenches for $d=2$, $n=4,5$, and for
$d=1$, $n=3,4,5$. We find, in agreement with previous simulations using
fixed-length spins, that dynamical scaling is obtained, with characteristic
length $L(t) = t^{1/2}$. We show that the asymptotic behaviour of the
structure-factor scaling function $g(q)$ is well fitted by the stretched
exponential form $g(q)\sim \exp(-bq^\delta)$, with an exponent $\delta$ that
appears to depend on both n and d. An analytical treatment of an approximate
large-N equation for the pair correlation function yields $g(q) \sim
q^{-(d-1)/2}\exp(-bq)$, with $b \sim (\ln n)^{1/2}$ for large $n$, in agreement
with recent simulations of the same equation.
