Delay differential equations in Haskell

README.md

ddeint.hs

Delay differential equations in Haskell

How to use

Download

Download ddeint.hs and a haskell compiler (in ubuntu: sudo apt install ghc)

Specify your ODE

In ddeint.hs, replace the following functions:

• dydt : a function that takes an array of the previous computed values and t, and returns the derivative of your function. For instance, if dy/dt = f(y(t-m)), write dydt y t = f(y(t-m))
• initialY : an list of historic values for y. For instance, initialY = [0,1,2] corresponds to
  • y(t0) = 0
  • y(t0-dt) = 1
  • y(t0 - 2dt) = 2

Compile

ghc -O2 ddeint.hs

run

./ddeint

ddeint.hs

import Data.List

dt = pi/100
t0 = 0
tmax = 50

dydt y t = y (t - 3*pi/2)

initialY = map sin [0, (-dt) .. (-2*pi) ]

--- Integrator
newval (oldYs, oldT) =
  let
    y t = oldYs !! round ((oldT - t)/dt)
    newY = (head oldYs) + dt * (dydt y oldT)
  in
    Just (newY, (newY:oldYs, oldT + dt))

integrated = unfoldr newval (initialY, t0)

--- Display results
main = sequence $ take (round ((tmax-t0)/dt)) $ map print integrated