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A Three-Point BVP of Time-Dependent Inverse Heat Source Problems and Solving by a TSLGSM

Weichung Yeih1,2, Chein-Shan Liu3
Computation and Simulation Center, Taiwan Ocean University, Keelung, Taiwan
Department of Harbor and River Engineering, Taiwan Ocean University, Keelung, Taiwan. Corresponding E-mail:
Department of Civil Engineering, Taiwan University, Taipei, Taiwan

Computer Modeling in Engineering & Sciences 2009, 46(2), 107-128.


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.


Inverse problem, Two-stage Lie-group shooting method, Time-dependent heat source

Cite This Article

Yeih, W., Liu, C. (2009). A Three-Point BVP of Time-Dependent Inverse Heat Source Problems and Solving by a TSLGSM. CMES-Computer Modeling in Engineering & Sciences, 46(2), 107–128.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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