RK4

A member of the Runge-Kutta method family, where:

$$\begin{array}{cc}\dot{y}& =f(t,y)\\ y_0& :=y(t_0)\end{array}$$

We then define interactive solutions using

$$\begin{array}{cl}{t}_{n+1}& =t_n+h\\ y_{n+1}& =y_n+\frac{h}{6}(k_1+2k_2+2k_3+k_4)\end{array}$$

where

• $h\in {\mathbb{R}}^{+}$ is the step size, chosen at the beginning
• $k_1=f(t_n,y_n)$
• $k_2=f(t_n+\frac{h}{2},y_n+h\frac{k_1}{2})$
• $k_3=f(t_n+\frac{h}{2},y_n+h\frac{k_2}{2})$
• $k_1=f(t_n,y_n+h{k}_3)$