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

Hongwu Zhang
2014 American Journal of Computational Mathematics  
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.
doi:10.4236/ajcm.2014.43018 fatcat:4wj22ufecrg2nhcg3kge75q2ki