# HIghly oscillatory solutions

1. Feb 23, 2010

### 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.

2. Feb 23, 2010

### gato_

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