Revision as of 00:49, 1 November 2005

Forth order Runge-Kutta Method

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

$\dot y = f\left( {x,y} \right)$

$k_1 = hf\left( {x_n ,y_n } \right)$

$k_2 = hf\left( {x_n + {h \over 2},y_n + {{k_1 } \over 2}} \right)$

$k_3 = hf\left( {x_n + {h \over 2},y_n + {{k_2 } \over 2}} \right)$

$k_4 = hf\left( {x_n + h,y_n + k_3 } \right)$

$y_{n + 1} = y_n + {{k_1 } \over 6} + {{k_2 } \over 3} + {{k_3 } \over 3} + {{k_4 } \over 6}$

@@ Line 1: / Line 1: @@
 = Forth order Runge-Kutta Method =
@@ Line 11: / Line 10: @@
 ::<math>k_4  = hf\left( {x_n  + h,y_n  + k_3 } \right) </math>
 ::<math>y_{n + 1}  = y_n  + {{k_1 } \over 6} + {{k_2 } \over 3} + {{k_3 } \over 3} + {{k_4 } \over 6} </math>
+----
+<i> Return to [[Numerical methods | Numerical Methods]] </i>