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A filter method with a priori and a posteriori parameter choice for the regularization of Cauchy problems for biharmonic equations

Authors: 

Tran Nhat Luan, Tran Thi Khieu, Tra Quoc Khanh*

Source title: 
Numerical Algorithms, 86: 1721-1746, 2020 (ISI)
Academic year of acceptance: 
2020-2021
Abstract: 

In the present paper, we devote our effort to Cauchy boundary value problems for biharmonic equations. In general, the investigated problem is ill-posed. Therefore, we develop a filter method to defeat the ill-posedness of the problem. Explicit convergence rate is established under both a priori and a posteriori parameter choice rules. Finally, a numerical example is presented to illustrate the ill-posedness of the problem as well as the effectiveness of the proposed method.