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題 名 | A Quasi-Boundary Semi-Analytical Method for Backward Heat Conduction Problems |
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作 者 | Chang, Chih-wen; Liu, Chein-shan; Chang, Jiang-ren; | 書刊名 | 中國工程學刊 |
卷 期 | 33:2 2010.03[民99.03] |
頁 次 | 頁163-175 |
分類號 | 335.21 |
關鍵詞 | Backward heat conduction problem; Ill-posed problem; Fredholm integral equation; Two-point boundary value problem; Regularized solution; Fourier series; |
語 文 | 英文(English) |
英文摘要 | Abstract In this paper, we propose a semi-analytical method to deal with the backward heat conduction problem due to a quasi-boundary idea. First of all, the Fourier series expansion technique is used to calculate the temperature field u(x, t) at any time t < T. Second, we consider a direct regularization by adding the term αu(x, 0) into the final time condition to obtain a type two Fredholm integral equation for u(x, 0). The termwise separable property of the kernel function allows us to transform the backward problem into a two-point boundary value problem and therefore, a closed-form solution is derived. The uniform convergence and error estimation of the regularized solution uα (x, t) are provided and a tactic to choose the regularized parameter is uggested. When several numerical examples are amenable, we discover that the present approach can retrieve all the past data very well and is robust even for seriously noised final data. |
本系統中英文摘要資訊取自各篇刊載內容。