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
