Runge-Kutta Methods

Defined as $y_{i+1}\approx y_i+\Delta t\cdot \varphi (t_i,y_i,\Delta t)$, where $\varphi$ is called the increment function, such that the simplest case of is $\varphi (t_i,y_i,\Delta t)=g(t_i,y_i)$ - the forward Euler method.