Weichung Yeih1,2, Chein-Shan Liu3
CMES-Computer Modeling in Engineering & Sciences, Vol.46, No.2, pp. 107-128, 2009, DOI:10.3970/cmes.2009.046.107
Abstract We consider an inverse problem for estimating an unknown time dependent heat source H(t) in a heat conduction equation ut(x,t) = uxx(x,t) + H(t). First this inverse problem is formulated as a three-point boundary value problem (BVP) for ODEs discretized from the transformed homogeneous governing equation. To treat this three-point BVP we develop a two-stage Lie-group shooting method (TSLGSM). The novel approach is examined through numerical examples to convince that it is rather accurate and efficient; the estimation error is small even for identifying discontinuous and oscillatory heat sources under noise. More >
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