A new wavelet method for solving an ill-posed problem

So far there are many papers which deal with the Cauchy problem for elliptic equation. However, most of them are devoted to the case of constant coefficients. In this paper, we consider a Cauchy problem for an elliptic equation with variable coefficients. Due to ill-posedness of this problem, we pro...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 203; no. 2; pp. 635 - 640
Main Author: Qian, Ailin
Format: Journal Article
Language:English
Published: New York, NY Elsevier Inc 15.09.2008
Elsevier
Subjects:
Elliptic equation
Error estimate
Exact sciences and technology
Fourier analysis
Inverse problems
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Partial differential equations
Regularization
Sciences and techniques of general use
Wavelet
Wavelet
Inverse problems
Elliptic equation
Regularization
Error estimate
Error estimation
Numerical linear algebra
Partial differential equation
Cauchy problem
Inverse problem
Exact solution
Regularization method
Wavelets
Numerical analysis
Wavelet transformation
Applied mathematics
Least squares method
Ill posed problem
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:So far there are many papers which deal with the Cauchy problem for elliptic equation. However, most of them are devoted to the case of constant coefficients. In this paper, we consider a Cauchy problem for an elliptic equation with variable coefficients. Due to ill-posedness of this problem, we provide a regularization method – wavelet dual least squares method to solve the problem. Via Meyer wavelet bases with a special project method dual least squares method, we can obtain error estimate between the regularized solution and exact solution.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2008.05.009