@Article{cmc.2011.024.209,
AUTHOR = {Chih-Wen Chang},
TITLE = {A New Quasi-Boundary Scheme for Three-Dimensional Backward Heat Conduction Problems},
JOURNAL = {Computers, Materials \& Continua},
VOLUME = {24},
YEAR = {2011},
NUMBER = {3},
PAGES = {209--238},
URL = {http://www.techscience.com/cmc/v24n3/22646},
ISSN = {1546-2226},
ABSTRACT = {In this study, we employ a semi-analytical scheme to resolve the three-dimensional backward heat conduction problem (BHCP) by utilizing a quasi-bound -ary concept. First, the Fourier series expansion method is used to estimate the temperature field u(x, y, z, t) at any time t < T. Second, we ponder a direct regularization by adding an extra term a(x, y, z, 0) to transform a second-kind Fredholm integral equation for u(x, y, z, 0). The termwise separable property of the kernel function allows us to acquire a closed-form regularized solution. In addition, a tactic to determine the regularization parameter is recommended. We find that the proposed method is robust and applicable to the three-dimensional BHCP when several numerical experiments are examined.},
DOI = {10.3970/cmc.2011.024.209}
}