TITLE:
Modified Tikhonov Method for Cauchy Problem of Elliptic Equation with Variable Coefficients
AUTHORS:
Hongwu Zhang
KEYWORDS:
Ill-Posed Problem, Cauchy Problem, Elliptic Equation with Variable Coefficients, Tikhonov Regularization Method, Convergence Estimates
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.4 No.3,
June
3,
2014
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.