Lie series algorithms and Runge-Kutta algorithms

For linear autonomous system, the Lie Series algorithms of order two and order four were proved to be respectively identical with the improved Euler algorithm of stage two and order two, and with the classical R-K algorithm of stage four and order four. And the Lei Series algorithms are illustrated to be identical with Taylor progression algorithms, but they have different values of practical application because of different calculation methods of differential coefficients. Finally, the superiority of Lie Series for approaching nonlinear system was demonstrated numerically.