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Curve Fitting Results

A typical set of results is shown in figure 7-17

   figure6133

where only every tenth result has been plotted. The wave was simulated using tex2html_wrap_inline16363 , tex2html_wrap_inline16365 and tex2html_wrap_inline12323 . The best fit curve through all the data points is also shown. The close agreement between the data points and the fitted curve can clearly be seen. A number of longer simulations were also run. These simulations were generally performed on a larger grid because of the high rate of damping observed when a wavelength of 256 lu is used. A typical example is shown in figure 7-18 which was simulated on a 512 by 512 grid. Only points every 400 time-steps have been marked. The wave was simulated with tex2html_wrap_inline16369 and tex2html_wrap_inline15795 . The wave was allowed to evolve for tex2html_wrap_inline16373 time-steps and was observed to oscillate for almost twelve periods in this time. The agreement between the results and the best fit curve through the points is good although the discrepancy becomes larger towards the end of the simulation when the amplitude of the waves is only a few lattice sites. The error is slightly larger than that found earlier when a shorter time period was considered. Here e = 2531 giving a root mean square deviation of 1.0 lu.



James Buick
Tue Mar 17 17:29:36 GMT 1998