A Herglotz wavefunction method for solving the inverse Cauchy problem connected with the Helmholtz equation

A Herglotz wavefunction method for solving the inverse Cauchy problem connected with the Helmholtz equation

This paper is concerned with the Cauchy problem connected with the Helmholtz equation. On the basis of the denseness of Herglotz wavefunctions, we propose a numerical method for obtaining an approximate solution to the problem. We analyze the convergence and stability with a suitable choice of regul...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of computational and applied mathematics 2013-01, Vol.237 (1), p.215-222
Hauptverfasser: Zhang, Deyue, Ma, Fuming, Zheng, Enxi
Format: Artikel
Sprache:eng
Schlagworte:
Approximation
Cauchy problem
Convergence
Helmholtz equation
Helmholtz equations
Herglotz wavefunctions
Inverse
Mathematical models
Regularization
Wavefunctions
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:This paper is concerned with the Cauchy problem connected with the Helmholtz equation. On the basis of the denseness of Herglotz wavefunctions, we propose a numerical method for obtaining an approximate solution to the problem. We analyze the convergence and stability with a suitable choice of regularization method. Numerical experiments are also presented to show the effectiveness of our method.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2012.07.026