A Tikhonov Regularization Method for Solving an Inverse Heat Source Problem

2018 ◽  
Vol 43 (1) ◽  
pp. 441-452
Author(s):  
Shuping Yang ◽  
Xiangtuan Xiong
Keyword(s):  
Heat Source ◽  
Tikhonov Regularization ◽  
Regularization Method ◽  
Tikhonov Regularization Method ◽  
Inverse Heat Source

OPTIMAL ERROR BOUND AND A GENERALIZED TIKHONOV REGULARIZATION METHOD FOR IDENTIFYING AN UNKNOWN SOURCE IN THE POISSON EQUATION

2013 ◽  
Vol 12 (01) ◽  
pp. 1450004
Author(s):  
AI-LIN QIAN ◽  
JIAN-FENG MAO
Keyword(s):  
Heat Source ◽  
Numerical Experiment ◽  
Tikhonov Regularization ◽  
Regularization Method ◽  
Stability Estimate ◽  
Tikhonov Regularization Method ◽  
Optimal Error ◽  
The Poisson Equation ◽  
Optimal Error Bound ◽  
Inverse Heat Source

In this note we prove a stability estimate for an inverse heat source problem. Based on the obtained stability estimate, we present a generalized Tikhonov regularization method and obtain the error estimate. Numerical experiment shows that the generalized Tikhonov regularization works well.

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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