Consistent numerical schemes for solving nonlinear inverse source problems with the gradient-type algorithms and the Newton–Kantorovich methods

The algorithms of solving the inverse source problem for systems of the production-destruction equations are considered. Consistent in the sense of the Lagrangian identity numerical schemes for solving direct and conjugate problems have been built. With the adjoint equations, the sensitivity operator and its discrete analogue have been constructed. It links the measured values perturbations with the perturbations of the model parameters. This operator transforms the inverse problem to a quasilinear form and allows applying the Newton–Kantorovich methods to it. The paper provides a numerical comparison of the gradient algorithms based on the consistent and inconsistent numerical schemes and the Newton–Kantorovich algorithm applied to solving the inverse source problem for the nonlinear Lorenz model.