@Article{icces.2007.003.069,
AUTHOR = {Chih-Wen  Chang, Chein-Shan  Liu, Jiang-Ren  Chang},
TITLE = {The Lie-Group Shooting Method for Quasi-Boundary Regularization of Backward Heat Conduction Problems},
JOURNAL = {The International Conference on Computational \& Experimental Engineering and Sciences},
VOLUME = {3},
YEAR = {2007},
NUMBER = {2},
PAGES = {69--80},
URL = {http://www.techscience.com/icces/v3n2/30670},
ISSN = {1933-2815},
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.},
DOI = {10.3970/icces.2007.003.069}
}