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Mathematical Problems in Engineering
Volume 2014, Article ID 917972, 9 pages
http://dx.doi.org/10.1155/2014/917972
Research Article

An Iterative Regularization Method to Solve the Cauchy Problem for the Helmholtz Equation

School of Science, Jiangnan University, Jiangsu Province, Wuxi 214122, China

Received 12 January 2014; Accepted 19 February 2014; Published 25 March 2014

Academic Editor: Rolf Stenberg

Copyright © 2014 Hao Cheng et al. 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

A regularization method for solving the Cauchy problem of the Helmholtz equation is proposed. The a priori and a posteriori rules for choosing regularization parameters with corresponding error estimates between the exact solution and its approximation are also given. The numerical example shows the effectiveness of this method.