  We provide a numerical validation method of blow-up solutions for finite
dimensional vector fields admitting asymptotic quasi-homogeneity at infinity.
Our methodology is based on quasi-homogeneous compactifications containing a
new compactification, which shall be called a quasi-parabolic compactification.
Divergent solutions including blow-up solutions then correspond to global
trajectories of associated vector fields with appropriate time-variable
transformation tending to equilibria on invariant manifolds representing
infinity. We combine standard methodology of rigorous numerical integration of
differential equations with Lyapunov function validations around equilibria
corresponding to divergent directions, which yields rigorous upper and lower
bounds of blow-up times as well as rigorous profile enclosures of blow-up
solutions.
