Numerical solution of boundary value problems can be performed by the usual finite difference or finite element methods and adequate space mesh. Monte Carlo methods can also be relevant; they lead, after equations discretization, to specific treatments related to domain local geometry. This work is also investigating another method which provides integral representations of the solution to stationary deterministic linear boundary value problems. In particular, the Dirichlet problem is known to have an integral representation which is used to obtain an algorithm which computes the solution by implementing a random walk simulation. The ensuing numerical methods do not require the storage of a grid discretization in computer memory. Programming is short, easy to check step by step; moreover, the implementation to a higher dimension requires but a few additional lines. More specifically, a stationary deterministic linear boundary value problem is to be solved with boundary condition of Fourier or mixed types. We show, in particular, using examples, that the boundary condition treatments can be reduced to the counting of absorptions and reflections on the boundaries.