  Hypoxy induced angiogenesis processes can be described coupling an
integrodifferential kinetic equation of Fokker-Planck type with a diffusion
equation for the angiogenic factor. We propose high order positivity preserving
schemes to approximate the marginal tip density by combining an asymptotic
reduction with weighted essentially non oscillatory and strong stability
preserving time discretization. We show that soliton-like solutions
representing blood vessel formation and spread towards hypoxic regions are
captured.
