TY  - EJOU
AU  - Chang, Chih-Wen  
AU  - Liu, Chein-Shan  
AU  - Chang, Jiang-Ren  

TI  - A Quasi-Boundary Semi-Analytical Approach for Two-Dimensional Backward Heat Conduction Problems
T2  - Computers, Materials \& Continua

PY  - 2010
VL  - 15
IS  - 1
SN  - 1546-2226

AB  - 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.
KW  - Backward heat conduction problem
KW  -  Ill-posed problem
KW  -  Fredholm integral equation
KW  -  Regularized solution
KW  -  Fourier series

DO  - 10.3970/cmc.2010.015.045