I came up with the following problem while using Euler-midpoint method and the classical fourth-order Runge-Kutta method to solve ordinary differential equations.
As step size $h$ decreases, which method is more efficient in estimation? Euler-midpoint method and the classical fourth-order Runge-Kutta method?
By solving several questions and comparing them to actual value given by exact solution, I realize that for the same step size $h$, the classical fourth-order Runge-Kutta method gives a more accurate estimation compared to the Euler-midpoint method.
However, does the same hold true as $h$ tends to $0$ from positive?