Journal
ADVANCES IN COMPUTATIONAL MATHEMATICS
Volume 34, Issue 2, Pages 167-183Publisher
SPRINGER
DOI: 10.1007/s10444-010-9148-1
Keywords
Tikhonov regularization; Reproducing Hilbert kernel; Inverse problem
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Funding
- Research Grants Council of the Hong Kong Special Administrative Region, China [CityU 101209]
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In this paper we propose a numerical reconstruction method for solving a backward heat conduction problem. Based on the idea of reproducing kernel approximation, we reconstruct the unknown initial heat distribution from a finite set of scattered measurement of transient temperature at a fixed final time. Standard Tikhonov regularization technique using the norm of reproducing kernel is adopt to provide a stable solution when the measurement data contain noises. Numerical results indicate that the proposed method is stable, efficient, and accurate.
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