# Runge Kutta methods

(Difference between revisions)
 Revision as of 00:49, 1 November 2005 (view source)Zxaar (Talk | contribs)← Older edit Revision as of 00:49, 1 November 2005 (view source)Zxaar (Talk | contribs) Newer edit → Line 1: Line 1: - = Forth order Runge-Kutta Method = = Forth order Runge-Kutta Method = Line 11: Line 10: ::$k_4 = hf\left( {x_n + h,y_n + k_3 } \right)$ ::$k_4 = hf\left( {x_n + h,y_n + k_3 } \right)$ ::$y_{n + 1} = y_n + {{k_1 } \over 6} + {{k_2 } \over 3} + {{k_3 } \over 3} + {{k_4 } \over 6}$ ::$y_{n + 1} = y_n + {{k_1 } \over 6} + {{k_2 } \over 3} + {{k_3 } \over 3} + {{k_4 } \over 6}$ + + + + + ---- + Return to [[Numerical methods | Numerical Methods]]

# Forth order Runge-Kutta Method

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

## Algorithm

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