An iterative algorithm for the backward heat conduction problem based on variable relaxation factors

摘要

In this paper, an iterative algorithm is proposed for solving the backward heat conduction problem (BHCP). The algorithm is based on allowing variable relaxation factors for an iterative algorithm proposed by Kozlov and Maz'ya [1]. The convergence of the relaxation algorithm is analysed both theoretically and numerically. The boundary element method (BEM) is used to implement numerically the algorithm and to show that the ill-posed BHCP is regularized by using an appropriate stopping criterion.