The homotopy method for identifying the radiative source term in the heat conduction problem. Issue 4 (2nd April 2016)

• Record Type: Journal Article
• Authors: Zhang, Wenyu; Ma, Fuming; Sun, Yao
• Is Part Of: Applicable analysis. Volume 95:Issue 4(2016)
• Page Start: 842
• Page End: 859
• Publication Date: 2016-04-02
• Subjects: inverse problem -- radiative coefficient -- homotopy method -- homotopy curve -- numerical experiments; 65M32; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2015.1037066
• Languages: English
• ISSNs: 0003-6811

Abstract

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.