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Added Forward Euler to Haskell #215

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Merged
merged 6 commits into from
Jul 8, 2018
Merged

Added Forward Euler to Haskell #215

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da1a022
Added Forward Euler in Haskell
Thurii Jul 4, 2018
eb1cd8d
Add explicit types and apply hindent
Thurii Jul 4, 2018
537be2c
Generalize solveEuler and checkResults
Thurii Jul 5, 2018
78ed76a
Further generalize checkResult and slim down solveEuler
Thurii Jul 6, 2018
0dd8148
Move timestep over to solveEuler
Thurii Jul 7, 2018
1a39112
Fix Typo
Thurii Jul 8, 2018
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Move timestep over to solveEuler
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@Thurii
Thurii committed Jul 7, 2018
commit 0dd8148ed9148debdc6ee2857df598933ab6cfd1
13 changes: 6 additions & 7 deletions chapters/differential_equations/euler/code/haskell/euler.hs
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Original file line number Diff line number Diff line change
@@ -1,21 +1,20 @@
solveEuler :: Num a => (a -> a) -> a -> [a]
solveEuler = iterate
solveEuler :: Num a => (a -> a) -> a -> a -> [a]
solveEuler f ts = iterate (\x -> x + f x * ts)

checkResult :: (Ord a, Num a, Num t, Enum t) => a -> (t -> a) -> [a] -> Bool
checkResult thresh check =
and . zipWith (\i k -> abs (check i - k) < thresh) [0..]

kinematics :: Double -> Double -> Double
kinematics timestep x = x - 3 * x * timestep
kinematics :: Double -> Double
kinematics x = -3 * x

main :: IO ()
main =
let timestep = 0.01
n = 100
threshold = 0.01
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adding a value for accFun:

accFun x = x - 3 * x * timestep
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Sould the acceleration function be:

accFun x = -3 * x
kinematics' = kinematics timestep
checkResult' = checkResult threshold $ exp . kinematics'
checkResult' = checkResult threshold $ exp . (\x -> x - 3 * x * timestep)
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I think here it should be (\x -> - 3 * x * timestep)
in putStrLn $
if checkResult' (take n $ solveEuler kinematics' 1)
if checkResult' (take n $ solveEuler kinematics timestep 1)
then "All values within threshold"
else "Value(s) not in threshold"