Newton type method is one of most popular methods for solving a large nonlinear algebraic system of equations arising from the discretization of partial differential equations with applications in science and engineering. Due to the presence of normal shock wave the convergence rate of Newton type methods for solving the discrete nozzle flow problem becomes very slow. In this thesis, we proposed and tested some right nonlinear preconditioned iterative algorithm to enhance robustness of Newton''s method and to improve it''s convergence rate. In this method, we define a local problem, which is governed by the same differential equation as the global problem we try to solve while the boundary conditions are imposed to satisfy the current global approximation at these grid points. Such solution of the local problem is able to quickly detect the exact location of shock wave. Finally, we show numerically that our approach is better than some traditional Newton''s method in terms of total CPU time.