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

• 作者: Hongwu Zhang
• 来源期刊: 美国计算数学期刊(英文)
• 学科: 数学
• 关键词: ILL-POSED PROBLEM Cauchy PROBLEM Elliptic Equation with Variable Coefficients Tikhonov Regularization METHOD Convergence Estimates
• 年，卷（期）: 2014,（3）
• 页码范围: 213-222
• 页数: 10页
• 分类号: O1

摘要

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.