An integral formulation procedure for the solutions to Helmholtz's equation in spherically symmetric media

Starting from Helmholtz's equation in inhomogeneous media, the associated radial second-order equation is investigated through a Volterra integral equation. First the integral equation is considered in a sphere. Boundedness, uniqueness and existence of the (regular) solution are established and the series form of the solution is provided. An estimate is determined for the error arising when the series is truncated. Next the analogous problem is considered for a spherical layer. Again, boundedness, uniqueness and existence of two base solutions are established and error estimates are determined. The procedure proves more effective in the sphere. Copyright (C) 2009 John Wiley & Sons, Ltd.