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.