Chein-Shan Liu1
CMES-Computer Modeling in Engineering & Sciences, Vol.47, No.1, pp. 1-22, 2009, DOI:10.3970/cmes.2009.047.001
Abstract In this paper an analytical method for approximating the solution of backward heat conduction problem is presented. The Fourier series expansion technique is used to formulate a first-kind Fredholm integral equation for the temperature field u(x,t) at any time t < T, when the data are specified at a final time T. Then we consider a direct regularization, instead of the Tikhonov regularization, by adding the term αu(x,t) to obtain a second-kind Fredholm integral equation. The termwise separable property of kernel function allows us by transforming it to a two-point boundary value problem, and thus a closed-form solution is derived.… More >
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