{-# OPTIONS_GHC -Wall #-} {-# LANGUAGE FlexibleContexts #-} {-# LANGUAGE Trustworthy #-} {- | Module : Physics.Learn.RungeKutta Copyright : (c) Scott N. Walck 2012-2014 License : BSD3 (see LICENSE) Maintainer : Scott N. Walck Stability : experimental Differential equation solving using 4th-order Runge-Kutta -} module Physics.Learn.RungeKutta ( rungeKutta4 , integrateSystem ) where import Physics.Learn.StateSpace ( StateSpace(..) , Diff , Time , (.+^) ) import Data.VectorSpace ( (^+^) , (*^) , (^/) ) -- | Take a single 4th-order Runge-Kutta step rungeKutta4 :: StateSpace p => (p -> Diff p) -> Time p -> p -> p rungeKutta4 f dt y = let k0 = dt *^ f y k1 = dt *^ f (y .+^ k0 ^/ 2) k2 = dt *^ f (y .+^ k1 ^/ 2) k3 = dt *^ f (y .+^ k2) in y .+^ (k0 ^+^ 2 *^ k1 ^+^ 2 *^ k2 ^+^ k3) ^/ 6 -- | Solve a first-order system of differential equations with 4th-order Runge-Kutta integrateSystem :: StateSpace p => (p -> Diff p) -> Time p -> p -> [p] integrateSystem systemDerivative dt = iterate (rungeKutta4 systemDerivative dt) {- -- | Take a single 4th-order Runge-Kutta step rungeKutta4 :: (VectorSpace v, Fractional (Scalar v)) => (v -> v) -> Scalar v -> v -> v rungeKutta4 f h y = let k0 = h *^ f y k1 = h *^ f (y ^+^ k0 ^/ 2) k2 = h *^ f (y ^+^ k1 ^/ 2) k3 = h *^ f (y ^+^ k2) in y ^+^ (k0 ^+^ 2 *^ k1 ^+^ 2 *^ k2 ^+^ k3) ^/ 6 -- | Solve a first-order system of differential equations with 4th-order Runge-Kutta integrateSystem :: (VectorSpace v, Fractional (Scalar v)) => (v -> v) -> Scalar v -> v -> [v] integrateSystem systemDerivative dt = iterate (rungeKutta4 systemDerivative dt) -}