Chih-Wen Chang1, Chein-Shan Liu2
CMES-Computer Modeling in Engineering & Sciences, Vol.59, No.3, pp. 239-274, 2010, DOI:10.3970/cmes.2010.059.239
Abstract In this article, we propose a backward group preserving scheme (BGPS) to tackle the multi-dimensional backward heat conduction problem (BHCP). The BHCP is well-known as severely ill-posed because the solution does not continuously depend on the given data. When eight numerical examples (including nonlinear and nonhomogeneous BHCP, and Neumann and Robin conditions of homogeneous BHCP) are examined, we find that the BGPS is applicable to the multi-dimensional BHCP. Even with noisy final data, the BGPS is also robust against disturbance. The one-step BGPS effectively reconstructs the initial data from the given final data, which with a suitable grid length produces… More >
Login
Register
