Numerical Method for a Cauchy Problem for Multi-Dimensional Laplace Equation with Bilateral Exponential Kernel

Xianli Lv and Xiufang Feng ()
Additional contact information
Xianli Lv: School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China
Xiufang Feng: School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China

Mathematics, 2023, vol. 11, issue 8, 1-20

Abstract: This study examined a Cauchy problem for a multi-dimensional Laplace equation with mixed boundary. This problem is severely ill-posed in the sense of Hadamard. To solve this problem, a mollification approach is suggested based on a bilateral exponential kernel and this is a new approach. The stable error estimates are obtained under the priori and posteriori rule, in which the numerical findings are much influenced by the unknown a priori information. An error estimate between the exact and regular solution is given. A numerical experiment of interest reveals that our procedure is efficient and stable for perturbation noise in the data.

Keywords: multi-Laplace equation; ill-posed; bilateral exponential kernel; Cauchy problem; error estimate; mollification method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/8/1855/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/8/1855/ (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:11:y:2023:i:8:p:1855-:d:1123073

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 ().