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Runge-Kutta method: Difference between revisions
Minor formatting changes. Using "strformat". Updated output.
m (→{{header|ALGOL W}}: Fix Trans template) |
(Minor formatting changes. Using "strformat". Updated output.) |
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Line 2,144:
let dy3 = step * fn(cur_t + 0.5 * step, cur_y + 0.5 * dy2)
let dy4 = step * fn(cur_t + step, cur_y + dy3)
import math, strformat
proc fn(t, y: float): float =
cur_y += (dy1 + 2.0 * (dy2 + dy3) + dy4) / 6.0▼
result = t * math.sqrt(y)
proc solution(t: float): float =
rk(start=0.0, stop=10.0, step=0.1)</lang>▼
result = (t^2 + 4)^2 / 16
proc rk(start, stop, step: float) =
let nsteps = int(round((stop - start) / step)) + 1
let delta = (stop - start) / float(nsteps - 1)
var cur_y = 1.0
for i in 0..<nsteps:
let cur_t = start + delta * float(i)
if abs(cur_t - math.round(cur_t)) < 1e-5:
echo &"y({cur_t}) = {cur_y}, error = {solution(cur_t) - cur_y}"
let dy1 = step * fn(cur_t, cur_y)
let dy2 = step * fn(cur_t + 0.5 * step, cur_y + 0.5 * dy1)
let dy3 = step * fn(cur_t + 0.5 * step, cur_y + 0.5 * dy2)
let dy4 = step * fn(cur_t + step, cur_y + dy3)
cur_y += (dy1 + 2.0 * (dy2 + dy3) + dy4) </lang>
{{out}}
<pre>y(0.0) = 1.0, error = 0.0
y(1.0) = 1.562499854278108, error = 1.457218921085968e-
y(2.0) = 3.9999990805208, error = 9.194792003341945e-
y(3.0) = 10.56249709043755, error = 2.909562448749625e-
y(4.0) = 24.99999376509064, error = 6.234909363911356e-
y(5.0) = 52.
y(6.0) = 99.99998340540358, error = 1.659459641700778e-
y(7.0) = 175.5624764822713, error = 2.351772874931157e-
y(8.0) = 288.9999684347986, error = 3.156520142510999e-
y(9.0) = 451.5624592768397, error = 4.07231603389846e-
y(10.0) = 675.9999490167097, error = 5.098329029351589e-
=={{header|Objeck}}==
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