The Spring-Damping Regularization Method and the Lie-Group Shooting Method for Inverse Cauchy Problems

摘要

The inverse Cauchy problems for elliptic equations, such as the Laplace equation, the Poisson equation, the Helmhokz 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 regu-larization 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.