A highly accurate homogeneous scheme for solving the laplace equation on a rectangular parallelepiped with boundary values in C k, 1

2012 ◽  
Vol 52 (6) ◽  
pp. 879-886 ◽  
Author(s):  
E. A. Volkov ◽  
A. A. Dosiyev
Keyword(s):  
Laplace Equation ◽  
Rectangular Parallelepiped ◽  
Boundary Values

scholarly journals Direct numerical identification of boundary values in the Laplace equation

2003 ◽  
Vol 152 (1-2) ◽  
pp. 161-174 ◽  
Author(s):  
Keisuke Hayashi ◽  
Kazuei Onishi ◽  
Yoko Ohura
Keyword(s):  
Laplace Equation ◽  
Boundary Values

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.

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