Generalized Tikhonov Method and Convergence Estimate for the Cauchy Problem of Modified Helmholtz Equation with Nonhomogeneous Dirichlet and Neumann Datum

Hongwu Zhang and Xiaoju Zhang
Additional contact information
Hongwu Zhang: School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China
Xiaoju Zhang: Development Center of Teachers’ Teaching, North Minzu University, Yinchuan 750021, China

Mathematics, 2019, vol. 7, issue 8, 1-19

Abstract: We investigate a Cauchy problem of the modified Helmholtz equation with nonhomogeneous Dirichlet and Neumann datum, this problem is ill-posed and some regularization techniques are required to stabilize numerical computation. We established the result of conditional stability under an a priori assumption for an exact solution. A generalized Tikhonov method is proposed to solve this problem, we select the regularization parameter by a priori and a posteriori rules and derive the convergence results of sharp type for this method. The corresponding numerical experiments are implemented to verify that our regularization method is practicable and satisfied.

Keywords: ill-posed problem; Cauchy problem; modified Helmholtz equation; generalized Tikhonov regularization method; convergence estimate (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/7/8/667/pdf (application/pdf)
https://www.mdpi.com/2227-7390/7/8/667/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:7:y:2019:i:8:p:667-:d:251785

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().