Zhang, H.W. (2011) Modified Quasi-Boundary Value Method for Cauchy Problems of Elliptic Equations with Variable Coefficients. Electronic Journal of Differential Equations, 106, 1-10.

has been cited by the following article:

• 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.