analytical - numerical model

What is the main difference between analytical approach and numerical approach?

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SeongMoon SEO wrote:

This is an obvious homework problem.
Consider the simple problem of a plane wave reflected off a planar boundary in an infinite space. This is trivial analytically, and impossible numerically. Now consider the problem of long-wavelength ocean waves scattered off a real coastline. This is impossible analytically but very doable numerically.
Generalize.
Cheers,
Phil Hobbs
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