Numerical approach for reconstructing an unknown source function in inverse parabolic problem

‎The inverse problem considered in this paper is devoted to reconstruction of the unknown source term in parabolic equation from additional information which is given by measurements at final time‎. ‎The cost functional is introduced and existence of the minimizer for this functional is established‎. ‎The numerical algorithm to solve the inverse problem is based on the Ritz-Galerkin method with shifted Legendre polynomials as basis functions‎. ‎Finally‎, ‎some numerical results are presented to demonstrate the accuracy and efficiency of the proposed method for test example‎.