A Wavelet Method for the Cauchy Problem for the Helmholtz Equation | Zendy

Fangfang Dou | Zendy; ChuLi Fu | Zendy

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A Wavelet Method for the Cauchy Problem for the Helmholtz Equation

Author(s) -

Fangfang Dou,

ChuLi Fu

Publication year - 2012

Publication title -

isrn applied mathematics

Language(s) - English

Resource type - Journals

eISSN - 2090-5572

pISSN - 2090-5564

DOI - 10.5402/2012/435468

Subject(s) - helmholtz equation , mathematics , wavelet , cauchy distribution , initial value problem , helmholtz free energy , mathematical analysis , cauchy problem , well posed problem , mathematical optimization , computer science , boundary value problem , physics , quantum mechanics , artificial intelligence

We consider a Cauchy problem for the Helmholtz equationat a fixed frequency. The problem is severely ill posed in thesense that the solution (if it exists) does not depend continuously onthe data. We present a wavelet method to stabilize the problem. Someerror estimates between the exact solution and its approximation aregiven, and numerical tests verify the efficiency and accuracy of the proposedmethod.

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