Having looked at 'Learn Physics by Programming in Haskell’ I became quite wobbly with excitement! :) So I took and implemented some of their ideas. My University level maths is around 40 years old and so I struggled with some of the later things - but it's slowly coming back! (I have a copy at https://github.com/banditpig/vectors/blob/master/LearnPhysics.pdf) So I have type Scalar = Double type XYZ = (Scalar, Scalar, Scalar) newtype Vector = V { xyz :: XYZ} and set of vector operations (^+^) :: Vector -> Vector -> Vector (^-^) :: Vector -> Vector -> Vector (*^) :: Scalar -> Vector -> Vector (^*) :: Vector -> Scalar -> Vector (^/) :: Vector -> Scalar -> Vector (>.<) :: Vector -> Vector -> Scalar -- dot (><) :: Vector -> Vector -> Vector -- cross etc I then have type Time = Double type Displacement = Vector type Velocity = Vector type State = (Time, Displacement, Velocity) eulerStep :: (State -> Vector) -> Double -> State -> State eulerStep f dt st@(t, r, v) = (t', r', v') where t' = t + dt r' = r ^+^ v ^* dt v' = v ^+^ f st ^* dt and so for a given acceleration function, time step and start state a solution is given by solution :: (State -> Vector) -> Double -> State -> [State] solution a dt = iterate (eulerStep a dt) What I'm trying to do is replace the Euler method of solving with the Rung-Kutta method. I'm really struggling in seeing how the Rung-Kutta examples I've seen are implemented using vectors. How should I progress? Any advice would be welcome! (I really want to implement it using the types I have rather than using an external library ) Many Thanks Mike