Startseite On regularization and error estimates for the Cauchy problem of the modified inhomogeneous Helmholtz equation
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On regularization and error estimates for the Cauchy problem of the modified inhomogeneous Helmholtz equation

  • Phan Trung Hieu EMAIL logo und Pham Hoang Quan
Veröffentlicht/Copyright: 21. Mai 2015

Abstract

In this paper, we consider the modified inhomogeneous Helmholtz equation Δu(x,y) -k2u(x,y) =f(x,y), x, 0 <y< 1, with inhomogeneous Cauchy data being given at y= 0. The problem is known to be ill-posed, as the solution (if exists) does not depend continuously on the given data. We propose a regularization method to obtain a stable approximate solution of the problem and get some error estimates. Finally, a numerical example shows the effectiveness of the proposed method.

Funding statement: This research has been supported by National Foundation of Scientific and Technology Development (Nafosted).

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Received: 2014-10-27
Revised: 2015-3-24
Accepted: 2015-4-24
Published Online: 2015-5-21
Published in Print: 2016-10-1

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