How can you prove that one step with Euler's method (a kind of Runge-Kutta method) gives a truncation error of order h^2 (i.e. O(h^2), where h is the step length)?
How can you prove that a bit more advanced Runge-Kutta method has the complexity order of the step error that it claims it has, for example the RK4 method?
I have wondered about this for a long time now but haven't come to any clarity with it.