Solution of BVPs in electrodynamics by stochastic methods

Field computation by the stochastic differential equation (SDE) method is demonstrated for electrostatic and electrodynamic propagation problems by considering simple examples. The solution to the inhomogeneous Helmholtz equation is first related to that a Schrodinger type of equation (parabolic in nature) by means of Laplace transformation. The SDE method is directly applied to this parabolic equation. Presence of the imaginary term in the parabolic equation warrants analytic continuation into the complex space that is addressed in this paper.