Discretized Tikhonov regularization by reproducing kernel Hilbert space for backward heat conduction problem

Authors:
Y. C. Hon;Tomoya Takeuchi
Affiliations:
Department of Mathematics, City University of Hong Kong, Hong Kong SAR, People's Republic of China;Center for Research in Scientific Computation, North Carolina State University, Raleigh, USA
Venue:
Advances in Computational Mathematics
Year:
2011

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Abstract

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.