@Article{cmc.2010.015.045,
AUTHOR = {Chih-Wen  Chang, Chein-Shan  Liu, Jiang-Ren  Chang},
TITLE = {A Quasi-Boundary Semi-Analytical Approach for Two-Dimensional Backward Heat Conduction Problems},
JOURNAL = {Computers, Materials \& Continua},
VOLUME = {15},
YEAR = {2010},
NUMBER = {1},
PAGES = {45--66},
URL = {http://www.techscience.com/cmc/v15n1/22530},
ISSN = {1546-2226},
ABSTRACT = {In this article, we propose a semi-analytical method to tackle the two-dimensional backward heat conduction problem (BHCP) by using a quasi-boundary idea. First, the Fourier series expansion technique is employed to calculate the temperature field u(<i>x, y, t</i>) at any time <i>t</i> < T. Second, we consider a direct regularization by adding an extra termau(<i>x, y, 0</i>) to reach a second-kind Fredholm integral equation for u(<i>x, y, 0</i>). The termwise separable property of the kernel function permits us to obtain a closed-form regularized solution. Besides, a strategy to choose the regularization parameter is suggested. When several numerical examples were tested, we find that the proposed scheme is robust and applicable to the two-dimensional BHCP.},
DOI = {10.3970/cmc.2010.015.045}
}