TY  - EJOU
AU  - Chang, Chih-Wen 

TI  - A New Quasi-Boundary Scheme for Three-Dimensional Backward Heat Conduction Problems
T2  - Computers, Materials \& Continua

PY  - 2011
VL  - 24
IS  - 3
SN  - 1546-2226

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

DO  - 10.3970/cmc.2011.024.209