173 



Fourier Component, (k) 







1 



2 



3 



4 



5 



6 



1=0 



- 



- 



- 



- 



- 



- 



- 



1=1 



5.0 



5.0 



5.0 



5.0 



5.0 



5.0 



5.0 



1=2 



5.5 



5.5 



5.8 



5.1 



6.2 



5.6 



6.2 



1=3 



5.0 



5.0 



5.0 



5.0 



5.0 



5.0 



5.1 



1=4 



4.6 



4.9 



6.1 



5.0 



5.8 



5.2 



5.3 



1=5 



4.9 



5.1 



4.8 



5.0 



5.1 



5.0 



5.0 



1=6 



5.0 



5.0 



5.1 



5.0 



5.0 



5.0 



5.3 



Table A. 5: Order of KFSBC errors for a standing wave computed to order 4 



Fourier Component, (k) 







1 



2 



3 



4 



5 



6 



1=0 



3.6 



5.0 



5.5 



5.0 



- 



5.0 



5.1 



1=1 



3.4 



5.0 



4.1 



5.0 



4.9 



5.0 



5.0 



1=2 



5.6 



5.0 



5.7 



5.0 



6.7 



5.4 



5.3 



1=3 



5.1 



5.0 



5.1 



5.0 



5.0 



5.0 



5.0 



1=4 



6.1 



5.2 



6.3 



5.0 



5.8 



5.5 



5.3 



1=5 



4.9 



5.0 



5.2 



5.1 



5.2 



5.0 



4.9 



1=6 



5.3 



5.0 



5.9 



5.0 



4.7 



5.0 



5.3 



Table A. 6: Order of DFSBC errors for a standing wave computed to order 4 



approximately fifth order for a standing wave. 



A. 4. 2 More Complex Seas 



Fenton's method relies on the periodicity of the solution to be tested. If the 

 solution is not periodic in space and time, then the errors in the boundary conditions 

 will not be periodic, and the Fourier expansion cannot be strictly applied. Fourier 

 coefficients could still be computed by assuming periodicity, but the discontinuity 

 generated by the assumption of periodicity would generate spurious results. These 

 could be minimized by taking a large number of points over a large range in time and 

 space, but this would become very computationally intensive. 



The accuracy of any approximate solution can be measured by examining the 



