EXPLANATION FILE OF PROGRAM TEQUDIF1
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The Runge-Kutta Method
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We present here the Runge-Kutta method of order 4 to integrate an ODE
of order 1: Y' = F(X, Y)
The development of Y around x coincidates with its Taylor development
n
of order 4:
y = y + h y' + (h^2/2) y" + (h^3/6) y"' + (h^4/24) y""
n+1 n n n n n
Other orders may also be used for the Runge-Kutta method, for instance
the Euler's method is a Runge-Kutta of order one.
Order 4 is often used because it is a good compromise between speed and
accuracy.
From a current point (x , y ), the next point is determined by:
n n
K = h f(x , y )
0 n n
k = h f(x + h/2, y + K /2)
1 n n 0
k = h f(x + h/2, y + K /2)
2 n n 1
k = h f(x + h, y + K )
3 n n 2
and y = y + (1/6)(K + 2 K + K )
n+1 n 0 1 3
It can be proved that the error at each step is about h^5.
The only drawback is the time of calculation: at each step, four function
evaluations are necessary.
From [BIBLI 03].
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End of file rkutta.txt.