An inversion method with decreasing regularization for the backward heat conduction problem

In this article an iterative algorithm is proposed for solving numerically the one-dimensional backward heat conduction problem (BHCP). The algorithm consists of using iteratively a least-squares fitting of the given data with a regularization term that decreases as the number of iterations increases. The algorithm is implemented using the boundary-element method (BEM). The convergence and the stability of the method are investigated for a severe test example, hence revealing the computational performance and limitations of the method proposed.