An inverse boundary problem for one-dimensional heat equation with a multilayer domain

In this paper, we propose a regularization method for determining a moving boundary from Cauchy data in one-dimensional heat equation with a multilayer domain. The numerical scheme is based on the use of the method of fundamental solutions and a discrete Tikhonov regularization technique. The generalized cross validation rule for the choice of a regularization parameter is applied to obtain a stable numerical approximation to the moving boundary. Numerical experiments for five examples show that our proposed method is effective and stable.