A computational method for inverse free boundary determination problem

Based on the method of fundamental solutions and discrepancy principle for the choice of location for source points, we extend in this paper the application of the computational method to determine an unknown free boundary of a Cauchy problem of parabolic‐type equation from measured Dirichlet and Neumann data with noises. The standard Tikhonov regularization technique with the L‐curve method for an optimal regularized parameter is adopted for solving the resultant highly ill‐conditioned system of linear equations. Both one‐dimensional and two‐dimensional numerical examples are given to verify the efficiency and accuracy of the proposed computational method.