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
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.
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.
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