3.1 Algorithm: Runge-Kutta Method of order 2

For the initial value problem (1.1) or (2.11), let $x_i=a+ih$, i=0,1,2..n where h is a given prescribed step size. set $y_0=y_0$. for $k=0,1,2...n-1$ define $y_{k+1}$ by

$$y_{k+1}=y_k+\frac{1}{2}(k_1+k_2),$$

where

$$k_1=hf(x_k,y_k)$$

$$k_2=hf(x_k+h,y_k+k_1)$$

The flow chart associated with the R-k method of order 2 is