A Wavelet Method for the Cauchy Problem for the Helmholtz Equation. (4th January 2012) - Dou, Fang-Fang
Abstract : We consider a Cauchy problem for the Helmholtz equation at a fixed frequency. The problem is severely ill posed in the sense that the solution (if it exists) does not depend continuously on the data. We present a wavelet method to stabilize the problem. Some error estimates between the exact solution and its approximation are given, and numerical tests verify the efficiency and accuracy of the proposed method.