A highly accurate LGSM for severely ill-posed BHCP under a large noise on the final time data
Resource
International Journal of Heat and Mass Transfer, 53(19-20), 4132-4140
Journal
International Journal of Heat and Mass Transfer
Pages
4132-4140
Date Issued
2010
Date
2010
Author(s)
Liu, Chein-Shan
Abstract
We consider a backward heat conduction problem (BHCP) in a slab, by subjecting to data at a final time, and some different type boundary conditions at two ends of the slab. The BHCP is known to be highly ill-posed. In order to numerically solve the BHCP we develop a new Lie-group shooting method (LGSM) in the spatial direction. It can retrieve very well the initial data with a high order accuracy. Several numerical examples of the BHCP demonstrate that the LGSM is applicable, even for those of strongly ill-posed ones with a large value of final time. Under the noisy final data the LGSM is robust against the disturbance. The new method is applicable for a severely ill-posed case with a final data very small in the order of 10-43, and the noise level is in the order of 10-1, of which the numerical solution still has an accuracy in the order of 10-2. The results are rather significant in the computations of BHCP. © 2010 Elsevier Ltd.
Type
journal article
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