This article proposes a new approximation scheme for quadratic-growth BSDEs in a
Markovian setting by connecting a series of semi-analytic asymptotic expansions applied
to short-time intervals. Although there remains a condition which needs to be checked
a posteriori, one can avoid altogether time-consuming Monte Carlo simulation and other
numerical integrations for estimating conditional expectations at each space-time node.
Numerical examples of quadratic-growth as well as Lipschitz BSDEs suggest that the
scheme works well even for large quadratic coefficients, and a fortiori for large Lipschitz