How will the modes change across the eddy whose SSP is shown in  (Sketch).

1. Consider the following eigenproblem:

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The exact eigenvalues are Professional Australia Essay Writers | AustraliaEssayWriting.com If we solve this problem using finite differences with the standard formula, we will get approximations to these eigenvalues Professional Australia Essay Writers | AustraliaEssayWriting.com 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 Professional Australia Essay Writers | AustraliaEssayWriting.com

c. Use Richardson extrapolation to estimate Professional Australia Essay Writers | AustraliaEssayWriting.com from these numbers in the limit Professional Australia Essay Writers | AustraliaEssayWriting.com

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 Professional Australia Essay Writers | AustraliaEssayWriting.com  requires roughly 20N operations.)