Considering the rigorous real-time computation of aero-engine non-linear model for on-board application in future

several iteration methods were studied in this paper.Their historical developments were surveyed

and convergence problems were discussed.Then a new improved method was presented in which the Jacobian matrix for a previous state point could be directly applied to the next point's calculation during the transition state simulation.It can improve execution efficiency of the model by reducing the number of aerothermodynamic model computations.Finally

a practical example has been simulated in these iteration methods respectively.The simulation results show that(1) the Broyden rank-one method has highest execution efficiency

so it's more suitable for non-linear aero-engine model real-time computing;(2) the improved method is simple and effective

laying a foundation for the rigorous real-time computation of aero-engine non-linear model.