Runge-Kutta method: Difference between revisions

=={{header|11l}}==

{{trans|Python}}

<lang 11l>F rk4(f, x0, y0, x1, n)

V vx = [0.0] * (n + 1)

V vy = [0.0] * (n + 1)

V h = (x1 - x0) / Float(n)

V x = x0

V y = y0

vx[0] = x

vy[0] = y

L(i) 1..n

V k1 = h * f(x, y)

V k2 = h * f(x + 0.5 * h, y + 0.5 * k1)

V k3 = h * f(x + 0.5 * h, y + 0.5 * k2)

V k4 = h * f(x + h, y + k3)

vx[i] = x = x0 + i * h

vy[i] = y = y + (k1 + k2 + k2 + k3 + k3 + k4) / 6

R (vx, vy)

F f(Float x, Float y) -> Float

R x * sqrt(y)

V (vx, vy) = rk4(f, 0.0, 1.0, 10.0, 100)

L(x, y) zip(vx, vy)[(0..).step(10)]

print(‘#2.1 #4.5 #2.8’.format(x, y, y - (4 + x * x) ^ 2 / 16))</lang>

{{out}}

<pre>

0.0 1.00000 0.00000000

1.0 1.56250 -1.45721892e-7

2.0 4.00000 -9.194792e-7

3.0 10.56250 -0.00000291

4.0 24.99999 -0.00000623

5.0 52.56249 -0.00001082

6.0 99.99998 -0.00001659

7.0 175.56248 -0.00002352

8.0 288.99997 -0.00003157

9.0 451.56246 -0.00004072

10.0 675.99995 -0.00005098

</pre>