I am trying to numerically evaluate an integral whose integrand depends on two parameters, say $(a,b)$ and when $b>>1$ I suspect (although it's not guaranteed) that the integrand is very small. Thus when $b>>1$ and I try to evaluate the integral Mathematica throws up ::slwcon errors suggesting it's either zero, rapidly oscillating or I need to increase precision. How can I get around this error to produce an actual result, even if it's ~10^-6.

**Some info on integrand**
the integrand looks like $\exp{(-ix)} W(x)$ where x is the integration variable. $W(x)$ is a function that I only know numerically. I compute it by using NDSolve to solve a second order ODE (specifically the radial part of the Klein Gordon equation in Schwarzschild as given by eq (4) of http://arxiv.org/abs/1106.2709) to get modes $u_i$ (which are oscillatory waves), then *roughly* I hit them with their cc $u_i u_i^*$  and sum them up to get $W$. 

I did some plots of the integrand and it is indeed oscillatory. Especially at large $b$ where it is super oscillatory.