During the simulations the height of the interface, above the bottom boundary,
was found every forty time-steps at the centre of the wave, 
.
The height of the wave was taken to be the height of the
highest site containing the denser fluid. This
gives a time series record of the wave height at the centre which
was then fitted to a curve of the form
This was done using a modified Gauss-Newton algorithm [82, 83]
where the parameters 
and c are the parameters found by the fitting process.
The sum of the square of the deviation of the data from the fitted curve, e,
was also computed and this gives a measure of the accuracy of the
cure fitting process and the fitted parameters.
The two
parameters in which we are interested are the frequency 
and the
damping parameter 
. The fitted parameter c should correspond to
the mwl 
which was used in initialising the wave. In practice it is shifted
slightly, particularly when 
is large and the interface has a significant thickness. The curve fitting process was applied using an
equation of the form
where is fixed and the other parameters are found as before. The results
obtained for and were found to be within 1% of their
previous values. The value of e was increased by
, where N is the number of points.
This means that e is no longer a good measure of
the goodness of fit of the other parameters. Thus it was decided to include
c in the set of fitted parameters. Similarly the value of A should be
related to the initial deformation amplitude. It is, however, slightly
different, again due to the interface thickness. If A is fixed,
in equation (7.1), to an incorrect value there is little
effect on but a significant effect on .
If A is set too large the value found for can be seen to be too large, the values of the fitted curve being greater then
the data points for small times and smaller than the data points for large
times. If A is set too small the value of is correspondingly too
small. Thus it is important that A has the correct value and this is best achieved by allowing it to be found by the fitting routine.
A phase difference 
is also included in equation (7.1).
This accounts for any discrepancy in the initialisation procedure. The main
error in the initialisation is the profile of the density and the
order parameter at the interface. The
values found for were no larger then 1% of 
suggesting that the initialisation method is adequate.
The average value found for e from over a hundred different waves,
each with either 1,000 or 900 data points, was found to be 85. This corresponds to an
RMS difference between the data and the fitted curve of 0.31 lattice units.
