Explicit, three-stage, third-order, variable-step, Runge-Kutta method.[^1]
```math
\frac{dy}{dt} = f(t, y)
```
```math
t_{n+1} = t_n + h
```
```math
k_1 = f(t_n, y_n)
```
```math
k_2 = f(t_n + \tfrac{1}{2} h, y_n + \tfrac{1}{2} h k_1)
```
```math
k_3 = f(t_n + \tfrac{3}{4} h, y_n + \tfrac{3}{4} h k_2)
```
```math
y_{n+1} = y_n + \frac{h}{9}\left(2k_1 + 3k_2 + 4k_3\right)
```
```math
k_4 = f(t_{n+1}, y_{n+1})
```
```math
e_{n+1} = \frac{h}{72}\left(-5k_1 + 6k_2 + 8k_3 - 9k_4\right)
```