A self-adaptive LGSM to recover initial condition or heat source of one-dimensional heat conduction equation by using only minimal boundary thermal data
Resource
International Journal of Heat and Mass Transfer, 54(7-8), 1305-1312
Journal
International Journal of Heat and Mass Transfer
Pages
1305-1312
Date Issued
2011
Date
2011
Author(s)
Liu, Chein-Shan
Abstract
The present study is concerned with the recovery of an unknown initial condition for a one-dimensional heat conduction equation by using only the usual two boundary conditions of the direct problem for heat equation. The algorithm assumes a function for the unknown initial condition and derives an inverse problem for estimating a spatially-dependent heat source F(x) in T t(x, t) = Txx(x, t) + F(x). A self-adaptive Lie-group shooting method, namely a Lie-group adaptive method (LGAM), is developed to find F(x), and then by integrations or by solving a linear system we can extract the information for unknown initial condition. The new method possesses twofold advantages in that no a priori information of unknown functions is required and no extra data are needed. The accuracy and efficiency of present method are confirmed by comparing the estimated results with some exact solutions. © 2010 Elsevier Ltd. All rights reserved.
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Type
journal article
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