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3.1 Algorithm: Runge-Kutta Method of order 2

For the initial value problem (1.1.1) or (2.1.1), let $x_i=a+ih$, i=0,1,2, .....n where h is a given prescribed step size set . For define $y_{k+1}$ by $y_0=y_0$

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

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 :

 

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