  The dark matter annihilation channels sometimes involve sharp resonances. In
such cases the usual momentum averaged approximations for computing the DM
abundance may not be accurate. We develop an easily accessible momentum
dependent framework for computing the DM abundance accurately and efficiently
near such features. We apply the method to the case of a singlet scalar dark
matter $s$ interacting with SM through higgs portal $\lambda_{\rm hs}s^2 h^2$
and compare the results with different momentum averaged methods. The accuracy
of the latter depend strongly on the strength of the elastic interactions and
corrections are large if WIMP has negligible interactions beyond the main
annihilation channel. In the singlet scalar model however, the standard model
scatterings induce an efficient kinetic equilibrium that validates the momentum
averaged computation to 20 per cent accuracy. We update the current extent of
the allowed region in the light singlet scalar dark matter to $m_{\rm S} \in
[56,62.5]$ GeV.
