a numerical algorithm based on chebyshev polynomials for solving some inverse source problems

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 ofthese 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 approximatesolutions.