Numerical Method for a Cauchy Problem for Multi-Dimensional Laplace Equation with Bilateral Exponential Kernel
-
Published:2023-04-13
Issue:8
Volume:11
Page:1855
-
ISSN:2227-7390
-
Container-title:Mathematics
-
language:en
-
Short-container-title:Mathematics
Author:
Lv Xianli1ORCID,
Feng Xiufang1
Affiliation:
1. School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China
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.
Funder
National Natural Science Foundation of China
Natural Science Foundation of Ningxia
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference30 articles.
1. Tikhonov, A.N., and Arsenin, V.Y. (1977). Solutions of Ill-Posed Problems, Winson.
2. On the inverse potential problem of electrocardiology;Magenes;Calcolo,1980
3. Stable determination of a crack from boundary measurements;Alessandrini;Proc. R. Soc. Edinb.,1993
4. Hadamard, J. (1923). Lectures on the Cauchy Problem in Linear Partial Differential Equations, Yale University Press.
5. Stability and regularization of a discrete approximation to the Cauchy problem for Laplace’s equation;Reinhardt;SIAM J. Numer. Anal.,1999