Chih-Wen Chang1, Chein-Shan Liu2, Jiang-Ren Chang3
CMC-Computers, Materials & Continua, Vol.15, No.1, pp. 45-66, 2010, DOI:10.3970/cmc.2010.015.045
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(x, y, t) at any time t < T. Second, we consider a direct regularization by adding an extra termau(x, y, 0) to reach a second-kind Fredholm integral equation for u(x, y, 0). 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,… More >
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