افشین بابائی

‎In this paper‎ , two inverse problems of determining an unknown source term in a parabolic‎ equation are considered‎ . First‎, ‎ the unknown source term is ‎ estimated in the form of a combination of Chebyshev functions‎ . ‎ Then‎ , ‎ a numerical algorithm based on Chebyshev polynomials is presented for obtaining the solution of the problem‎ . ‎ For solving the problem‎ , ‎ the operational matrices of integration and derivation are introduced and utilized to reduce the mentioned problem into the matrix equations which correspond to a system of linear algebraic equations with unknown Chebyshev coefficients‎ . Due‎ to ill-posedness of these inverse problems‎ , ‎ the Tikhonov regularization method with generalized cross validation (GCV) criterion is applied to find stable‎ solutions.‎ ‎ Finally‎ , some examples are presented to illustrate the efficiency of this numerical method‎ . The numerical results show that the proposed method is a reliable method and can give high accuracy approximate