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    <ol> <li><p>Lists are not the best datastructure for this type of code (with lots of (++), and (last)). You lose a lot of time constucting and deconstructing lists. I'd use Data.Sequence or arrays, as in C versions.</p></li> <li><p>There is no chance for thunks of makeu0 to be garbage-collected, since you need to retain all of them (well, all of the results of "diffuse", to be exact) all the way till the end of computation in order to be able to do "reverse" in applyBC. Which is very expensive thing, considering that you only need two items from the tail of the list for your "zeroflux". </p></li> </ol> <p>Here is fast hack of you code that tries to achieve better list fusion and does less list (de)constructing:</p> <pre><code>module Euler1D ( stepEuler ) where -- impose zero flux condition zeroflux mu (boundary:inner:xs) = boundary+mu*2*(inner-boundary) -- one step of integration stepEuler mu n = (applyBC . (diffused mu)) $ makeu0 n where diffused mu (left:x:[]) = [] -- ignore outer points diffused mu (left:x:right:xs) = -- integrate inner points let y = (x+mu*(left+right-2*x)) in y `seq` y : diffused mu (x:right:xs) applyBC inner = lbc + sum inner + rbc -- boundary conditions where lbc = zeroflux mu ((f 0 n):inner) -- left boundary rbc = zeroflux mu ((f n n):(take 2 $ reverse inner)) -- right boundary -- initial condition makeu0 n = [ f x n | x &lt;- [0..n]] f x n = ((^2) . sin . (pi*) . xi) x where xi x = fromIntegral x / fromIntegral n </code></pre> <p>For 200000 points, it completes in 0.8 seconds vs 3.8 seconds for initial version</p>
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    1. COThank you very much! This is exactly kind of answer I was looking for. I didn't know about Data.Sequence and arrays, but suspected, that it is possible to avoid lots of list operations. P.S. y `seq` y:… in diffused is a nice pattern… also take's in applyBC… Thank you!
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    2. COThough, summation in stepEuler changes the original semantics of the function. I restored the original semantics (http://pastebin.com/f5ca77a7f) and it still runs reasonably fast (0.5 seconds for 2e5 points). I'll consider using Data.Sequence now.
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