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The method of fundamental solutions for the inverse heat source problem. (English) Zbl 1244.80026
Summary: 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.
80M25Other numerical methods (thermodynamics)
80A23Inverse problems (thermodynamics)
80A20Heat and mass transfer, heat flow
65M80Fundamental solutions, Green’s function methods, etc. (IVP of PDE)