9.5 Méthode de Runge Kutta

1. méthode Runge Kutta d'ordre 2
   $$\begin{eqnarray*} k_{1} & = & f(x_{n},y_{n})\\ k_{2} & = & f(x_{n}+\frac{h}{2},y_{n}+\frac{h}{2}k_{1})\\ y_{n+1} & = & y_{n}+hk_{2}\end{eqnarray*}$$
   
   
   
   
   variante:
   
   $$\begin{eqnarray*} k_{1} & = & f(x_{n},y_{n})\\ k_{2} & = & f(x_{n}+h,y_{n}+hk_{1})\\ y_{n+1} & = & y_{n}+\frac{h}{2}(k_{1}+k_{2})\end{eqnarray*}$$
   
   
   
   

2. méthode Runge Kutta d'ordre 4
   $$\begin{eqnarray*} k_{1} & = & f(x_{n},y_{n})\\ k_{2} & = & f(x_{n}+\frac{h}{2},... ...3})\\ y_{n+1} & = & y_{n}+\frac{h}{6}(k_{1}+2k_{2}+2k_{3}+k_{4})\end{eqnarray*}$$