This paper is concerned with the problem of simulation of (Xt)0≤t≤T , thesolution of a stochastic differential equation constrained by some boundary conditions in a smooth domainD: namely, we consider the case where the boundary ∂D is killing, or where it is instantaneouslyreflecting in an oblique direction. Given N discretization times equally spaced on the interval [0,T],we propose new discretization schemes: they are fully implementable and provide a weak error of orderN -1 under some conditions. The construction of these schemes is based on a natural principle of localapproximation of the domain into a half space, for which efficient simulations are available.
