TY  - EJOU
AU  - Liu, Chein-Shan  
AU  - Kuo, Chung-Lun  
AU  - Liu, Dongjie  

TI  - The Spring-Damping Regularization Method and the Lie-Group Shooting Method for Inverse Cauchy Problems
T2  - Computers, Materials \& Continua

PY  - 2011
VL  - 24
IS  - 2
SN  - 1546-2226

AB  - The inverse Cauchy problems for elliptic equations, such as the Laplace equation, the Poisson equation, the Helmholtz equation and the modified Helmholtz equation, defined in annular domains are investigated. The outer boundary of the annulus is imposed by overspecified boundary data, and we seek unknown data on the inner boundary through the numerical solution by a spring-damping regularization method and its Lie-group shooting method (LGSM). Several numerical examples are examined to show that the LGSM can overcome the ill-posed behavior of inverse Cauchy problem against the disturbance from random noise, and the computational cost is very cheap.
KW  - Lie-group shooting method
KW  -  Elliptic equations
KW  -  Inverse Cauchy problem
KW  -  Ill-posed problem
KW  -  Spring-damping regularization method

DO  - 10.3970/cmc.2011.024.105