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

DOI: 10.4236/ajcm.2014.43018   PDF   HTML   XML   2,908 Downloads   3,809 Views   Citations

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.

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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.

Conflicts of Interest

The authors declare no conflicts of interest.

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