A Wavelet Method for the Cauchy Problem for the Helmholtz Equation

Fang-Fang Dou, Chu-Li Fu
2012 ISRN Applied Mathematics  
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.
doi:10.5402/2012/435468 fatcat:t4yvkzsgf5fp5iusxqzubffaae