Computing zeros of analytic functions in the complex plane without using derivatives Original Research Article

We present a package in Fortran 90 which solves image, where image without requiring the evaluation of derivatives, image. image is bounded by a simple closed curve and image must be holomorphic within image.We have developed and tested the package to support our work in the modeling of high frequency and optical wave guiding and resonant structures. The respective eigenvalue problems are particularly challenging because they require the high precision computation of all multiple complex roots of image confined to the specified finite domain. Generally image, despite being holomorphic, does not have explicit analytical form thereby inhibiting evaluation of its derivatives.