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ABSTRACT

The Lie-Group Shooting Method for Quasi-Boundary Regularization of Backward Heat Conduction Problems

Chih-Wen Chang1, Chein-Shan Liu2, Jiang-Ren Chang1

Department of Systems Engineering and Naval Architecture, National Taiwan Ocean University, Keelung 20224, Taiwan.
Department of Mechanical and Mechatronic Engineering, National Taiwan Ocean University, Keelung 20224, Taiwan. Corresponding author, E-mail address: csliu@mail.ntou.edu.tw

The International Conference on Computational & Experimental Engineering and Sciences 2007, 3(2), 69-80. https://doi.org/10.3970/icces.2007.003.069

Abstract

By using a quasi-boundary regularization we can formulate a two-point boundary value problem of the backward heat conduction equation. The ill-posed problem is analyzed by using the semi-discretization numerical schemes. Then, the resulting ordinary differential equations in the discretized space are numerically integrated towards the time direction by the Lie-group shooting method to find the unknown initial conditions. The key point is based on the erection of a one-step Lie group element G(T) and the formation of a generalized mid-point Lie group element G(r). Then, by imposing G(T) = G(r) we can seek the missing initial conditions through a minimum discrepancy of the target in terms of the weighting factor r ∈ (0, 1). A numerical example is worked out to persuade that this novel approach has good efficiency and accuracy.

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Cite This Article

Chang, C., Liu, C., Chang, J. (2007). The Lie-Group Shooting Method for Quasi-Boundary Regularization of Backward Heat Conduction Problems. The International Conference on Computational & Experimental Engineering and Sciences, 3(2), 69–80. https://doi.org/10.3970/icces.2007.003.069



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