Numerical Integration of Functions of a Rapidly Rotating Phase
Numerical Integration of Functions of a Rapidly Rotating Phase
We present an algorithm for the efficient numerical evaluation of integrals of the form $I(\omega) = \int_0^1 F( x,\e^{\i \omega x}; \omega) \, \d x$ for sufficiently smooth but otherwise arbitrary $F$ and $\omega \gg 1$. The method is entirely “black-box,” i.e., it does not require the explicit computation of …