# Numerical Methods: Mid Point Higher Order ODEs

I am taking a Numerical Methods class and the professor told us to find out how to solve Higher Order Ordinary Differential Equations using the midpoint method. As of right now, I only know how to use the midpoint method for solving 2nd Order equations but I wouldn't know how to solve anything higher than that.

I've searched for a while but haven't found anything. Can anyone point me in the right direction?

• Convert it to a system of ODE of the first order en.wikipedia.org/wiki/… – uranix May 20 '15 at 14:27
• The explicit midpoint method for $y'=f(t,y)$ is $y_{n+1}=y+h·f(t_n+h/2,y+h/2·f(t_n,y_n))$. The implicit midpoint method combines one step of the implicit followed by one of the explicit Euler method. – LutzL May 20 '15 at 14:37