@Article{cmes.2011.077.057,
AUTHOR = {Chein-Shan  Liu, Chung-Lun  Kuo},
TITLE = {A Spring-Damping Regularization and a Novel Lie-Group Integration Method for Nonlinear Inverse Cauchy Problems},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {77},
YEAR = {2011},
NUMBER = {1},
PAGES = {57--80},
URL = {http://www.techscience.com/CMES/v77n1/25712},
ISSN = {1526-1506},
ABSTRACT = {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.},
DOI = {10.3970/cmes.2011.077.057}
}