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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    2,703 Downloads   3,495 Views   Citations
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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.

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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