A Three-Point BVP of Time-Dependent Inverse Heat Source Problems and Solving by a TSLGSM
Weichung Yeih;,; and Chein-Shan Liu;

doi:10.3970/cmes.2009.046.107
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 46, No. 2, pp. 107-128, 2009
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Keywords Inverse problem, Two-stage Lie-group shooting method, Time-depen -dent heat source
Abstract We consider an inverse problem for estimating an unknown time-depen -dent 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.
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