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A regularization method for solving the radially symmetric backward heat conduction problem

Authors
Journal
Applied Mathematics Letters
0893-9659
Publisher
Elsevier
Volume
30
Identifiers
DOI: 10.1016/j.aml.2013.12.009
Keywords
  • Ill-Posed Problem
  • Backward Heat Equation
  • Regularization
  • Error Estimate

Abstract

Abstract This work is devoted to solving the radially symmetric backward heat conduction problem, starting from the final temperature distribution. The problem is ill-posed: the solution (if it exists) does not depend continuously on the given data. A modified Tikhonov regularization method is proposed for solving this inverse problem. A quite sharp estimate of the error between the approximate solution and the exact solution is obtained with a suitable choice of regularization parameter. A numerical example is presented to verify the efficiency and accuracy of the method.

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