A source term estimation in an inverse problem by conjugate gradient method

In this paper, a non-linear source term is estimated for an inverse parabolic problem using noisy 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 of polynomial basis function for the source term estimation. To examine the accuracy of estimations, a test example is carried out. The algorithm can return good numerical estimations for the unknowns very fast