A method of [[Iterative Numerical Integration]] for solving [[Differential Equations]]. $\huge z_{i+1} = z_{i} + hf\pa{ t_{i} + \frac{h}{2}, z_{i} + \frac{h}{2}f(t_{i},z_{i}) } $ For a given step $h\in \R$. $\huge \begin{align} k_{1} &= f(t_{i},z_{i}) \\ k_{2} &= f\left( t_{i} + \frac{h}{2}, z_{i}+\frac{h}{2}k_{1} \right) \end{align} $ This method is a type of [[Runge-Kutta Methods|Runge-Kutta Method]], hence it has a [[Butcher Tableau]] of the following: $\huge \begin{array}{c|cccc} & k_{1}&k_{2} \\ \hline 0 & \\ \frac{1}{2} & \frac{1}{2} & \\ \hline &0 & 1 \end{array} $