  We review, implement, and compare numerical integration schemes for spatially
bounded diffusions stopped at the boundary which possess a convergence rate of
the discretization error with respect to the timestep $h$ higher than ${\cal
O}(\sqrt{h})$. We address specific implementation issues of the most
general-purpose of such schemes. They have been coded into a single Matlab
program and compared, according to their accuracy and computational cost, on a
wide range of problems in up to ${\mathbb R}^{48}$. The paper is self-contained
and the code will be made freely downloadable.
