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

Hongwu Zhang

doi:10.4236/ajcm.2014.43018

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AJCM> Vol.4 No.3, June 2014

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

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DOI: 10.4236/ajcm.2014.43018 2,798 Downloads 3,646 Views Citations

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Hongwu Zhang

Affiliation(s)

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

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.

Cite this paper

Zhang, H. (2014) Modified Tikhonov Method for Cauchy Problem of Elliptic Equation with Variable Coefficients. American Journal of Computational Mathematics, 4, 213-222. doi: 10.4236/ajcm.2014.43018.

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