An inverse heat conduction problem with a nonlinear source term

• Published in: Nonlinear analysis Vol. 65; no. 3; pp. 615 - 621
• Main Authors: Shidfar, A., Karamali, G.R., Damirchi, J.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01-08-2006; Elsevier
• Subjects: Chebyshev polynomial; Direct and inverse heat conduction problem; Exact sciences and technology; Implicit finite difference approximation; Least-squares method; Mathematical analysis; Mathematics; Partial differential equations; Residual minimization; Sciences and techniques of general use; Direct and inverse heat conduction problem; Least-squares method; Residual minimization; 35R30; Chebyshev polynomial; Implicit finite difference approximation; Direct problem; Source terms; Direct and inverse heat conduction problem; Residual minimization; Chebyshev polynomial; Least-squares method; Implicit finite difference approximation; Least squares method; Nonlinear analysis; Nonlinear problems; Heat flux; Finite difference method; Inverse problem
• ISSN: 0362-546X; 1873-5215
• DOI: 10.1016/j.na.2005.09.030

In this paper, the nonlinear problem of an inhomogeneous heat equation with linear boundary conditions will be considered. The surface heat flux history of a heated conducting body will be identified. The approach of the proposed method is to approximate the unknown function using linear polynomial pieces which are determined consecutively from the solution of the minimization problem on the basis of overspecified data. Some numerical examples will also be presented.