The application of Itô's formula induces some probabilistic representations of solutions of deterministic linear problems with boundary conditions of Dirichlet, Neumann, Fourier, and mixed types. These representations are used to establish some easily implementable algorithms which compute an approximate solution by means of simulation of reflected random walks. The boundary condition treatment can be reduced to the counting of absorptions and reflections on the boundaries. We recall first this simulation method and compare numerically some Euler's and Runge-Kutta's schemes used to solve boundary value problems. Secondly, we consider the heat problem with superabundant data on the boundary.