A Wavelet Method for the Cauchy Problem for the Helmholtz Equation. (4th January 2012)

• Record Type: Journal Article
• Authors: Dou, Fang-Fang; Fu, Chu-Li
• Other Names: Bellouquid A. Academic Editor.; Marin L. Academic Editor.
• Is Part Of: ISRN applied mathematics. Volume 2012(2012)
• Publication Date: 2012-01-04
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; Electronic journals; 510
• DOI: 10.5402/2012/435468
• Languages: English
• ISSNs: 2090-5564

Abstract

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.