A meshless method for reconstructing the heat source and partial initial temperature in heat conduction

Abstract

In this article, we use the method of fundamental solutions to reconstruct the heat source and part of the initial temperature simultaneously in one-dimensional heat conduction problem. This problem is ill-posed, thus a Tikhonov regularization method with generalized cross-validation criterion is applied to obtain a stable numerical solution. Numerical experiments for several examples show that the proposed method is reasonable and feasible.

Keywords:

• ill-posed problem
• the method of fundamental solution
• Tikhonov regularization method
• inverse source problem
• backward heat conduction equation

AMS Subject Classifications::

• 65N20
• 65N80

Acknowledgements

The author would like to thank the referees and editors for their careful reading and valuable suggestions that improved the quality of our article. The work described in this article was supported by the NNSF of China (10971089).