  We propose a new class of asymptotic preserving schemes to solve kinetic
equations with mono-kinetic singular limit. The main idea to deal with the
singularity is to transform the equations by appropriate scalings in velocity.
In particular, we study two biologically related kinetic systems. We derive the
scaling factors and prove that the rescaled solution does not have a singular
limit, under appropriate spatial non-oscillatory assumptions, which can be
verified numerically by a newly developed asymptotic preserving scheme. We set
up a few numerical experiments to demonstrate the accuracy, stability,
efficiency and asymptotic preserving property of the schemes.
