In this article, we propose a new numerical computation scheme for Markovian backward
stochastic differential equations (BSDEs) by connecting the semi-analytic short-term
approximation applied to each time interval, which has a very simple form to implement.
We give the error analysis for BSDEs which have generators of quadratic growth
with respect to the control variables and bounded terminal conditions. Although the
scheme requires higher regularities than the standard method, one can avoid altogether
time-consuming Monte Carlo simulation or other numerical integration for estimating
conditional expectations at each space-time node. We provide numerical examples of
quadratic-growth (qg) BSDEs as well as standard Lipschitz BSDEs to illustrate the proposed scheme and its empirical convergence rate.