Excellence in Research and Innovation for Humanity

Zhenyu Zhao

Publications

2

Publications

2
892
Identifying an Unknown Source in the Poisson Equation by a Modified Tikhonov Regularization Method
Abstract:

In this paper, we consider the problem for identifying the unknown source in the Poisson equation. A modified Tikhonov regularization method is presented to deal with illposedness of the problem and error estimates are obtained with an a priori strategy and an a posteriori choice rule to find the regularization parameter. Numerical examples show that the proposed method is effective and stable.

Keywords:
Ill-posed problem, Unknown source, Poisson equation, Tikhonov regularization method, Discrepancy principle
1
9760
Fourier Spectral Method for Analytic Continuation
Abstract:

The numerical analytic continuation of a function f(z) = f(x + iy) on a strip is discussed in this paper. The data are only given approximately on the real axis. The periodicity of given data is assumed. A truncated Fourier spectral method has been introduced to deal with the ill-posedness of the problem. The theoretic results show that the discrepancy principle can work well for this problem. Some numerical results are also given to show the efficiency of the method.

Keywords:
Analytic continuation, ill-posed problem, regularization method Fourier spectral method, the discrepancy principle.