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Runge Kutta methods

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Forth order Runge-Kutta Method

The fourth order Runge-Kutta method could be summarized as:

Algorithm

\dot y = f\left( {x,y} \right)
k_1  = hf\left( {x_n ,y_n } \right)
k_2  = hf\left( {x_n  + {h \over 2},y_n  + {{k_1 } \over 2}} \right)
k_3  = hf\left( {x_n  + {h \over 2},y_n  + {{k_2 } \over 2}} \right)
k_4  = hf\left( {x_n  + h,y_n  + k_3 } \right)
y_{n + 1}  = y_n  + {{k_1 } \over 6} + {{k_2 } \over 3} + {{k_3 } \over 3} + {{k_4 } \over 6}




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