Open Access

ARTICLE

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

Weichung Yeih^1,2, Chein-Shan Liu³
1 Computation and Simulation Center, Taiwan Ocean University, Keelung, Taiwan
2 Department of Harbor and River Engineering, Taiwan Ocean University, Keelung, Taiwan. Corresponding E-mail: wcyeih@mail.ntou.edu.tw
3 Department of Civil Engineering, Taiwan University, Taipei, Taiwan

Computer Modeling in Engineering & Sciences 2009, 46(2), 107-128. https://doi.org/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 u_t(x,t) = u_xx(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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Keywords

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

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