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

TI  - A Spring-Damping Regularization and a Novel Lie-Group Integration Method for Nonlinear Inverse Cauchy Problems
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2011
VL  - 77
IS  - 1
SN  - 1526-1506

AB  - In this paper, the solutions of inverse Cauchy problems for quasi-linear elliptic equations are resorted to an unusual mixed group-preserving scheme (MGPS). The bottom of a finite rectangle is imposed by overspecified boundary data, and we seek unknown data on the top side. The spring-damping regularization method (SDRM) is introduced by converting the governing equation into a new one, which includes a spring term and a damping term. The SDRM can further stabilize the inverse Cauchy problems, such that we can apply a direct numerical integration method to solve them by using the MGPS. Several numerical examples are examined to show that the SDRM+MGPS can overcome the ill-posed behavior of the inverse Cauchy problem. The present algorithm has good efficiency and stability against the disturbance from random noise, even with an intensity being large up to 10%, and the computational time is very saving.
KW  - Inverse Cauchy problem
KW  -  Quasi-linear elliptic equations
KW  -  Spring-damping regularization method
KW  -  Mixed group-preserving scheme

DO  - 10.3970/cmes.2011.077.057