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A wavelet method for the Cauchy problem for the Helmholtz equation. (English) Zbl 1264.65181

Summary: We consider a Cauchy problem for the Helmholtz equation at a fixed frequency. The problem is severely ill posed in the sense that the solution (if it exists) does not depend continuously on the data. We present a wavelet method to stabilize the problem. Some error estimates between the exact solution and its approximation are given, and numerical tests verify the efficiency and accuracy of the proposed method.

MSC:

65N20 Numerical methods for ill-posed problems for boundary value problems involving PDEs
74J20 Wave scattering in solid mechanics
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65T60 Numerical methods for wavelets
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