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Modified Tikhonov Method for Cauchy Problem of Elliptic Equation with Variable Coefficients
School of Mathematics and Information Science, Beifang University of Nationalities, Yinchuan, China
- 1 School of Mathematics and Information Science, Beifang University of Nationalities, Yinchuan, China
American Journal of Computational Mathematics·Volume 04 (2014)·Pages 213–222·Published 17 April 2014·DOI10.4236/ajcm.2014.43018
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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.
KeywordsIll-Posed ProblemCauchy ProblemElliptic Equation with Variable CoefficientsTikhonov Regularization MethodConvergence Estimates
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