This paper is concerned with the Cauchy problem connected with the Helmholtz equation. On the basis of the denseness of Herglotz wavefunctions, we propose a numerical method for obtaining an approximate solution to the problem. We analyze the convergence and stability with a suitable choice of regularization method. Numerical experiments are also presented to show the effectiveness of our method. © 2012 Elsevier B.V. All rights reserved.
Zhang, D., Ma, F., & Zheng, E. (2013). A Herglotz wavefunction method for solving the inverse Cauchy problem connected with the Helmholtz equation. Journal of Computational and Applied Mathematics, 237(1), 215–222. https://doi.org/10.1016/j.cam.2012.07.026