A modified Tikhonov regularization method based on Hermite expansion for solving the Cauchy problem of the Laplace equation

Abstract

In this paper, a Cauchy problem for the Laplace equation is considered. We develop a modified Tikhonov regularization method based on Hermite expansion to deal with the ill posed-ness of the problem. The regularization parameter is determined by a discrepancy principle. For various smoothness conditions, the solution process of the method is uniform and the convergence rate can be obtained self-adaptively. Numerical tests are also carried out to verify the effectiveness of the method.

Keywords

• cauchy problem for laplace equation
• ill-posed problem
• tikhonov regularization
• hermite approximation
• discrepancy principle
• 65d15
• 65n21
• 65n35