| Abstract: |
| We propose a new class of asymptotic preserving schemes to solve kinetic equations with a mono-kinetic singular limit. The main idea in dealing with 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 conducted a few numerical experiments demonstrating the schemes` accuracy, stability, efficiency, and asymptotic preserving properties. |
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