Table of Contents
ISRN Applied Mathematics
Volume 2012 (2012), Article ID 435468, 18 pages
http://dx.doi.org/10.5402/2012/435468
Research Article

A Wavelet Method for the Cauchy Problem for the Helmholtz Equation

1School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China
2School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China

Received 16 August 2011; Accepted 28 September 2011

Academic Editors: A. Bellouquid and L. Marin

Copyright © 2012 Fang-Fang Dou and Chu-Li Fu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.