What is this physics simulation formula doing? I have encountered a piece of code that performs a physics simulation of a moving projectile. I'm trying to understand what the mathematical basis is for a bit that looks like this:
$$
d_1 = f(x)
$$
$$
d_2 = f(x + \frac{d_1}{2})
$$
$$
d_3 = f(x + \frac{d_2}{2})
$$
$$
d_4 = f(x + d_3)
$$
$$
d = \frac{d_1 + 2 \cdot d_2 + 2 \cdot d_3 + d_4}{6}
$$
What is the name of this mathematical concept? It's obviously some sort of weighted average. The code uses real-world measured values, so it might be related to probability. This type of thing is hard to Google.

It's precisely the fourth-order Runge-Kutta method applied to the ordinary differential equation $\dfrac{\mathrm dx}{\mathrm dt}=f(x)$ with step size $h=1$.
