Using C in comparison with Mathematica software for solving an inverse source problem

In this paper , a nonlinear source term is approximated for an inverse parabolic problem using final observations as additional data . The inverse problem is solved as an optimization problem where objective function is minimized by the iterative Conjugate Gradient Method (CGM) . To examine the accuracy of approximations , some test examples are carried out . The algorithm can return good numerical approximations for the unknowns vary fast using C in comparison to Mathematica software