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An LGEM to Identify Time-Dependent Heat Conductivity Function by an Extra Measurement of Temperature Gradient

Chein-Shan Liu1,2

Department of Mechanical and Mechatronic Engineering,Taiwan Ocean University, Keelung, Taiwan
Department of Harbor and River Engineering, Tai-wan Ocean University, Keelung, Taiwan.E-mail:

Computers, Materials & Continua 2008, 7(2), 81-96.


We consider an inverse problem for estimating an unknown heat conductivity parameter α(t) in a heat conduction equation Tt(x,t) = α(t)Txx(x,t) with the aid of an extra measurement of temperature gradient on boundary. Basing on an establishment of the one-step Lie-group elements G(r) and G(l) for the semi-discretization of heat conduction equation in time domain, we can derive algebraic equations from G(r) = G(l). The new method, namely the Lie-group estimation method (LGEM), is examined through numerical examples to convince that it is highly accurate and efficient; the maximum estimation error is smaller than 10-5 for smooth parameter and for discontinuous and oscillatory parameter the accuracy is still in the order of 10-2. Although the estimation is carried out under a large measurement noise, the LGEM is also stable.


Cite This Article

C. Liu, "An lgem to identify time-dependent heat conductivity function by an extra measurement of temperature gradient," Computers, Materials & Continua, vol. 7, no.2, pp. 81–96, 2008.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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