The method of fundamental solutions for the inverse heat source problem

In this paper a meshless numerical scheme for solving the inverse heat source problem is proposed. The numerical solution is developed by using the fundamental solution of the heat equation as a basis function. Since the resulting matrix equation is badly ill-conditioned, a regularized solution is obtained by employing the Tikhonov regularization method, while the choice of the regularization parameter is based on generalized cross-validation criterion. Both continuous and discontinuous numerical examples are given to verify the efficiency and accuracy of the proposed computational method.