The fourth-order Runge-Kutta, RK4, which we will employ in the solution of various differential equations below, has the following algorithm $$k_1=hf(t_i,y_i) \hspace{0.5cm} k_2=hf(t_i+h/2,y_i+k_1/2)$$ $$k_3=hf(t_i+h/2,y_i+k_2/2)\hspace{0.5cm} k_4=hf(t_i+h,y_i+k_3)$$ with the final result $$y_{i+1}=y_i +\frac{1}{6}\left( k_1 +2k_2+2k_3+k_4\right).$$ Thus, the algorithm consists in first calculating $k_1$ with $t_i$, $y_1$ and $f$ as inputs. Thereafter, we increase the step size by $h/2$ and calculate $k_2$, then $k_3$ and finally $k_4$. The global error goes as $O(h^4)$.