Determination of a source term and boundary heat flux in an inverse heat equation

Abstract

In this paper, the determination of the heat source and heat flux at x = in one-dimensional inverse heat conduction problem (IHCP) is investigated. First with an suitable transformation, the problem is reduced, then the method of fundamental solutions (MFS) is used to solve the problem. Due to ill-posed the IHCP, the Tikhonov regularization method with Generalized cross validation (GCV) criterion are employed in numerical procedure. Finally, some numerical examples are presented to show the accuracy and effectiveness of the algorithm.