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

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

27 Scopus Citations
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Author(s)

  • Y. C. Hon
  • Tomoya Takeuchi

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)167-183
Journal / PublicationAdvances in Computational Mathematics
Volume34
Issue number2
Publication statusPublished - 2011

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. © 2010 Springer Science+Business Media, LLC.

Research Area(s)

  • Inverse problem, Reproducing Hilbert kernel, Tikhonov regularization