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zetafunction
Feb23-10, 05:19 AM
are there numerical mehtods or similar to obtain highly oscillatory solutions ?

i mean, given the solution to a certain differential equation

y(x)= (x^{1/2}+1)sin(10000000000000x)

could it be 'detected' by the numerical method used, for example when you get the solution you would see a highly oscillating part , due to the frequency being very very high.

gato_
Feb23-10, 03:36 PM
There are several options. Look for multiple scale method, the WKB approximation, and averaging methods