# Why the staggered Euler (Euler-Backward) method is not runge-kutta method?

Why the staggered Euler (Euler-Backward) method is not runge-kutta method?

The method is given by $$x_{n+1}=x_n+hg(p_{n+1})$$ $$p_{n+1}=p_n+hg(x_n)$$

I am not very familiar with the conditions of the Runge-kutta method, can someone help me with this? thank you.

• Why should it be considered by that name? The Wikipedia article on Runge-Kutta methods gives a nice outline of the original fourth-order explicit method and its generalizations to higher-order, adaptive, and mixed implicit-explicit methods (none of which would bring the comparatively primitive Euler backward method under this umbrella). – hardmath Mar 26 '16 at 22:03
• You may be interested in the Wikipedia article LIst of Runge-Kutta methods, which does mention backward Euler (under implicit methods). I think the intent (if one exists for a collectively authored post) is to present this first-order method "for comparison". – hardmath Mar 26 '16 at 22:16

Reordered as $$p_{n+1}=p_n+hg(x_n) \\ x_{n+1}=x_n+hf(p_{n+1})$$ your method is one of the variants of the symplectic Euler methods, which can also be classified under partitioned Runge-Kutta methods.