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Convergence Estimates for Some Regularization Methods to Solve a Cauchy Problem of the Laplace Equation

Convergence Estimates for Some Regularization Methods to Solve a Cauchy Problem of the Laplace Equation

Year:    2011

Numerical Mathematics: Theory, Methods and Applications, Vol. 4 (2011), Iss. 4 : pp. 459–477

Abstract

In this paper, we give a general proof on convergence estimates for some regularization methods to solve a Cauchy problem for the Laplace equation in a rectangular domain. The regularization methods we considered are: a non-local boundary value problem method, a boundary Tikhonov regularization method and a generalized method. Based on the conditional stability estimates, the convergence estimates for various regularization methods are easily obtained under the simple verifications of some conditions. Numerical results for one example show that the proposed numerical methods are effective and stable.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.2011.m1015

Numerical Mathematics: Theory, Methods and Applications, Vol. 4 (2011), Iss. 4 : pp. 459–477

Published online:    2011-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

Keywords:    Cauchy problem Laplace equation regularization methods convergence estimates.

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