How will the modes change across the eddy whose SSP is shown in (Sketch).
1. Consider the following eigenproblem:
The exact eigenvalues are 
If we solve this problem using finite differences with the standard formula, we will get approximations to these eigenvalues 
where N is the number of points in the mesh and k D 1; : : : ;N _ 1:
a. How can we use our formula for ˇk.N / to obtain a similar result for the approximate eigenvalues of an isovelocity acoustic problem?
b. Calculate 
c. Use Richardson extrapolation to estimate 
from these numbers in the limit 
d. Roughly, how large would N have to be to obtain this value by simple mesh
refinement?
e. How much slower would the mesh refinement be? (Solving the finite difference equations for 
requires roughly 20N operations.)
