@Article{cmes.2009.046.107,
AUTHOR = {Weichung  Yeih, Chein-Shan  Liu},
TITLE = {A Three-Point BVP of Time-Dependent Inverse Heat Source Problems and Solving by a TSLGSM},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {46},
YEAR = {2009},
NUMBER = {2},
PAGES = {107--128},
URL = {http://www.techscience.com/CMES/v46n2/25345},
ISSN = {1526-1506},
ABSTRACT = {We consider an inverse problem for estimating an unknown time dependent heat source <i>H(t)</i> in a heat conduction equation <i>u<sub>t</sub>(x,t)</i> = <i>u<sub>xx</sub>(x,t)</i> + <i>H(t)</i>. 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.},
DOI = {10.3970/cmes.2009.046.107}
}