On the Cauchy Problem for the Three-Dimensional Laplace Equation

2021 ◽  
Vol 65 (2) ◽  
pp. 49-64
Author(s):  
A. B. Khasanov ◽  
F. R. Tursunov
Keyword(s):  
Cauchy Problem ◽  
Laplace Equation ◽  
Three Dimensional ◽  
The Cauchy Problem

On the Cauchy problem for the three-dimensional Laplace equation

2021 ◽  
pp. 56-73
Author(s):  
Aknazar Bekdurdievich Khasanov ◽  
◽  
Farkhod Ruzikulovich Tursunov ◽  
Keyword(s):  
Cauchy Problem ◽  
Laplace Equation ◽  
Three Dimensional ◽  
The Cauchy Problem

scholarly journals A modified Tikhonov regularization method based on Hermite expansion for solving the Cauchy problem of the Laplace equation

2020 ◽  
Vol 18 (1) ◽  
pp. 1685-1697
Author(s):  
Zhenyu Zhao ◽  
Lei You ◽  
Zehong Meng
Keyword(s):  
Cauchy Problem ◽  
Laplace Equation ◽  
Tikhonov Regularization ◽  
Regularization Method ◽  
Regularization Parameter ◽  
Solution Process ◽  
Tikhonov Regularization Method ◽  
Hermite Expansion ◽  
The Cauchy Problem ◽  
Ill Posed

Abstract In this paper, a Cauchy problem for the Laplace equation is considered. We develop a modified Tikhonov regularization method based on Hermite expansion to deal with the ill posed-ness of the problem. The regularization parameter is determined by a discrepancy principle. For various smoothness conditions, the solution process of the method is uniform and the convergence rate can be obtained self-adaptively. Numerical tests are also carried out to verify the effectiveness of the method.

scholarly journals On a numerical solution of the Cauchy problem for the Laplace equation by the fundamental solutions method

PAMM ◽  
2007 ◽  
Vol 7 (1) ◽  
pp. 2040035-2040036
Author(s):  
Takashi Ohe ◽  
Katsu Yamatani ◽  
Kohzaburo Ohnaka
Keyword(s):  
Cauchy Problem ◽  
Numerical Solution ◽  
Laplace Equation ◽  
Fundamental Solutions ◽  
The Cauchy Problem
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