@Article{cmc.2008.007.081,
AUTHOR = {Chein-Shan Liu},
TITLE = {An LGEM to Identify Time-Dependent Heat Conductivity Function by an Extra Measurement of Temperature Gradient},
JOURNAL = {Computers, Materials \& Continua},
VOLUME = {7},
YEAR = {2008},
NUMBER = {2},
PAGES = {81--96},
URL = {http://www.techscience.com/cmc/v7n2/23453},
ISSN = {1546-2226},
ABSTRACT = {We consider an inverse problem for estimating an unknown heat conductivity parameter <i>α(t)</i> in a heat conduction equation <i>T<sub>t</sub>(x,t) = α(t)T<sub>xx</sub>(x,t)</i> with the aid of an extra measurement of temperature gradient on boundary. Basing on an establishment of the one-step Lie-group elements <b>G</b>(r) and <b>G</b>(l) for the semi-discretization of heat conduction equation in time domain, we can derive algebraic equations from <b>G</b>(r) = <b>G</b>(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<sup>-5</sup> for smooth parameter and for discontinuous and oscillatory parameter the accuracy is still in the order of 10<sup>-2</sup>. Although the estimation is carried out under a large measurement noise, the LGEM is also stable.},
DOI = {10.3970/cmc.2008.007.081}
}