Numerical source term approximation in an inverse problem by an iterative method

In this paper, a non-linear 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). Sensitivity analysis is used to find a suitable basis functions group from a polynomial basis function for the source term approximation. To examine the accuracy of approximations, a test example is carried out.