An optimal filtering method for the Cauchy problem of the Helmholtz equation

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Abstract

In this paper, we consider a Cauchy problem for the Helmholtz equation in a rectangle. An optimal filtering method is presented for approximating the solution of this problem, and the Hölder type error estimate is obtained. Numerical illustration shows that the method works effectively.

Keywords

Cauchy problem for the Helmholtz equation
Filtering regularization
Error estimate
Ill-posed problem

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The project is supported by the NNSF of China (Nos. 10671085, 10971089).