@Article{cmes.2010.059.239,
AUTHOR = {Chih-Wen  Chang, Chein-Shan  Liu},
TITLE = {A Backward Group Preserving Scheme for Multi-Dimensional Backward Heat Conduction Problems},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {59},
YEAR = {2010},
NUMBER = {3},
PAGES = {239--274},
URL = {http://www.techscience.com/CMES/v59n3/25503},
ISSN = {1526-1506},
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 a highly accurate solution never seen before. The results are very important in the computations of multi-dimensional BHCP.},
DOI = {10.3970/cmes.2010.059.239}
}