  We deal with Mckean-Vlasov and Boltzmann type jump equations. This means that
the coefficients of the stochastic equation depend on the law of the solution,
and the equation is driven by a Poisson point measure with intensity measure
which depends on the law of the solution as well. In [3], Alfonsi and Bally
have proved that under some suitable conditions, the solution $X_t$ of such
equation exists and is unique. One also proves that $X_t$ is the probabilistic
interpretation of an analytical weak equation. Moreover, the Euler scheme
$X_t^{\mathcal{P}}$ of this equation converges to $X_t$ in Wasserstein
distance. In this paper, under more restricted assumptions, we show that the
Euler scheme $X_t^{\mathcal{P}}$ converges to $X_t$ in total variation distance
and $X_t$ has a smooth density (which is a function solution of the analytical
weak equation). On the other hand, in view of simulation, we use a truncated
Euler scheme $X^{\mathcal{P},M}_t$ which has a finite numbers of jumps in any
compact interval. We prove that $X^{\mathcal{P},M}_{t}$ also converges to $X_t$
in total variation distance. Finally, we give an algorithm based on a particle
system associated to $X^{\mathcal{P},M}_t$ in order to approximate the density
of the law of $X_t$. Complete estimates of the error are obtained.
