Can Numerical Methods Handle Highly Oscillatory Solutions?

[zetafunction]

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_]

There are several options. Look for multiple scale method, the WKB approximation, and averaging methods