Application of successive approximation method to the computation of the Green's function in axisymmetric inhomogeneous media

The successive approximation method (SAM) is applied to the computation of the Green's function in axisymmetric inhomogeneous media, SAM is implemented by using an iterative procedure that produces a series, and the series is proven to be a Taylor series. The condition of the convergence is derived from the theory of functions of several complex variables. In each iteration, the Fourier-Hankel transform and its inverse are applied to the approximation of some order of the Green's function and the result is the approximation one order higher than the original. Fast Fourier-Hankel transform (FFHT) is employed to speed up the computation, and thereby, an algorithm SAM-FFHT is formulated.