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
. 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 ℝ48. The paper is self-contained and the code will be
made freely downloadable.