A numerical method for calculating Green's functions

A new method is presented for the numerical computation of the Green's function associated with a linear boundary value problem. The interpretation of the Green's function as the set of probabilities of a random walk from the interior points to the boundary points allows one to extend the method to complicated domains consisting of simple overlapping sub-regions, to take into account variations in the boundaries, and to simplify calculations at boundaries like an iron-air interface. An example illustrating the strength and accuracy for calculating Green's functions is described in detail in “The numerical solution of boundary value problems over an infinite domain”, Canadian Electrical Journal, Volume 1, Number 3, pp. 18–20, July 1976.