A MODIFIED TIKHONOV REGULARIZATION METHOD FOR THE CAUCHY PROBLEM OF LAPLACE EQUATION

doi:10.1016/S0252-9602(15)30058-8

Abstract

Abstract:

In this paper, we consider the Cauchy problem for the Laplace equation, which is severely ill-posed in the sense that the solution does not depend continuously on the data. A modified Tikhonov regularization method is proposed to solve this problem. An error estimate for the a priori parameter choice between the exact solution and its regularized approximation is obtained. Moreover, an a posteriori parameter choice rule is proposed and a stable error estimate is also obtained. Numerical examples illustrate the validity and effectiveness of this method.

Key words: Cauchy problem for Laplace equation, ill-posed problem, a posteriori parameter choice, error estimate

CLC Number:

35R25

Fan YANG, Chuli FU, Xiaoxiao LI. A MODIFIED TIKHONOV REGULARIZATION METHOD FOR THE CAUCHY PROBLEM OF LAPLACE EQUATION[J].Acta mathematica scientia,Series B, 2015, 35(6): 1339-1348.

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