The homotopy method for identifying the radiative source term in the heat conduction problem

Abstract

In this paper, we discuss the inverse problem of identifying the radiative source term in a heat conductive equation from the measured final noisy temperature. We construct an algorithm in conjunction with the homotopy method, and give some theoretical details regarding the homotopy curve. The heat conductive equation is discretized via the finite difference method, and the coefficient estimation is formulated as the problem of finding the zeros of a nonlinear map. The homotopy method is applied to overcome the difficulty of traditional iterative methods which, usually, only converge if the initial guess is close enough to the exact solution (local convergence). To avoid the instability due to noisy measurements, the regularized homotopy method is introduced. At last, several numerical examples are presented to show the efficiency of the regularized homotopy method.

Keywords:

• inverse problem
• radiative coefficient
• homotopy method
• homotopy curve
• numerical experiments

AMS Subject Classification:

• 65M32

Acknowledgements

The authors are grateful to the anonymous referees for their valuable comments.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by the NSFC [grant number 11371172]; and the Fundamental Research Funds for the Central Universities [grant number 3122014K012].