Modified Tikhonov Method for Cauchy Problem of Elliptic Equation with Variable Coefficients

Hongwu Zhang

School of Mathematics and Information Science, Beifang University of Nationalities, Yinchuan, China.

DOI: 10.4236/ajcm.2014.43018                

Abstract

A Cauchy problem for the elliptic equation with variable coefficients is considered. This problem is severely ill-posed. Then, we need use the regularization techniques to overcome its ill-posedness and get a stable numerical solution. In this paper, we use a modified Tikhonov regularization method to treat it. Under the a-priori bound assumptions for the exact solution, the convergence estimates of this method are established. Numerical results show that our method works well.

Keywords

Ill-Posed Problem, Cauchy Problem, Elliptic Equation with Variable Coefficients, Tikhonov Regularization Method, Convergence Estimates

Conflicts of Interest

The authors declare no conflicts of interest.

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