Year: 2012
Communications in Mathematical Research , Vol. 28 (2012), Iss. 4 : pp. 300–312
Abstract
In this paper, we consider the reconstruction of the wave field in a bounded domain. By choosing a special family of functions, the Cauchy problem can be transformed into a Fourier moment problem. This problem is ill-posed. We propose a regularization method for obtaining an approximate solution to the wave field on the unspecified boundary. We also give the convergence analysis and error estimate of the numerical algorithm. Finally, we present some numerical examples to show the effectiveness of this method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2012-CMR-19033
Communications in Mathematical Research , Vol. 28 (2012), Iss. 4 : pp. 300–312
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Fourier moment method Cauchy problem Helmholtz equation regularization ill-possedness.