A Wavelet Method for the Cauchy Problem for the Helmholtz Equation

Abstract EN

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.