  This article deals with the numerical approximation of Markovian backward
stochastic differential equations (BSDEs) with generators of quadratic growth
with respect to $z$ and bounded terminal conditions. We first study a slight
modification of the classical dynamic programming equation arising from the
time-discretization of BSDEs. By using a linearization argument and BMO
martingales tools, we obtain a comparison theorem, a priori estimates and
stability results for the solution of this scheme. Then we provide a control on
the time-discretization error of order $\frac{1}{2}-\varepsilon$ for all
$\varepsilon>0$. In the last part, we give a fully implementable algorithm for
quadratic BSDEs based on quantization and illustrate our convergence results
with numerical examples.
