TY - EJOU AU - Liu, Chein-Shan TI - An LGEM to Identify Time-Dependent Heat Conductivity Function by an Extra Measurement of Temperature Gradient T2 - Computers, Materials \& Continua PY - 2008 VL - 7 IS - 2 SN - 1546-2226 AB - 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. KW - Inverse problem KW - Parameter identification KW - Lie-group estimation method KW - Time-dependent heat conductivity DO - 10.3970/cmc.2008.007.081