  In numerical simulations of binary neutron star systems, the equation of
state of the dense neutron star matter is an important factor in determining
both the physical realism and the numerical accuracy of the simulations. Some
equations of state used in simulations are $C^2$ or smoother in the
pressure/density relationship function, such as a polytropic equation of state,
but may not have the flexibility to model stars or remnants of different masses
while keeping their radii within known astrophysical constraints. Other
equations of state, such as tabular or piece-wise polytropic, may be flexible
enough to model additional physics and multiple stars' masses and radii within
known constraints, but are not as smooth, resulting in additional numerical
error. We will study in this paper a recently developed family of equation of
state, using a spectral expansion with sufficient free parameters to allow for
a larger flexibility than current polytropic equations of state, and with
sufficient smoothness to reduce numerical errors compared to tabulated or
piece-wise polytropic equations of state. We perform simulations at three mass
ratios with a common chirp mass, using two distinct spectral equations of
state, and at multiple numerical resolutions. We evaluate the gravitational
waves produced from these simulations, comparing the phase error between
resolutions and equations of state, as well as with respect to analytical
models. From our simulations we estimate that the phase difference at merger
for binaries with a dimensionless weighted tidal deformability difference
greater than $\Delta \tilde{\Lambda} = 55$ can be captured by the SpEC code for
these equations of state.
