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@0not
Last active August 29, 2015 14:16
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Numerically and analytically solve the radioactive decay problem (dN/dt = -kN) and plot the results.
module Main where
import Graphics.EasyPlot
dt = 0.001 -- Timestep
tau = 0.05 -- Decay constant
n0 = 1000 -- Initial number of particles
main = do
plot X11 $ [Data2D [Title "Euler", Color Red, Style Lines] [] numerical,
Data2D [Title "Actual", Color Blue, Style Lines] [] analytic]
-- Analytic results
analytic :: [(Double, Double)]
analytic = [(t, n0 * (exp (-t/tau))) | t <- [0.0, dt .. tau*5]]
-- Numerical results
numerical :: [(Double, Double)]
numerical = [(t, num t) | t <- [0.0, dt..tau*5]]
-- Numerically solve dN/dt = -kN
num :: Double -> Double
num t
| t > 0 = let t' = num (t - dt) in t' - dt / tau * t'
| otherwise = n0
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