Runge-Kutta method

Definition

can be either implicit or explicit

$$y_{k+1}=y_k+{\int }_{t_k}^{t_{k+1}}f(t,y)dt$$

explicit RK4

the most common Runge-Kutta scheme, 4-th order

$$y_{k+1}=y_k+\frac{h_k}{6}(k_1+k_2+k_3+k_4)$$