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Runge Kutta methods

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

Revision as of 00:49, 1 November 2005

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}




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