Math.Integrators.StormerVerlet

Documentation

integrateV

Arguments

:: PrimMonad m

=> Integrator a

Internal integrator

-> a

initial value

-> Vector Double

vector of time points

-> m (Vector a)

vector of solution

Integrate ODE equation using fixed steps set by a vector, and returns a vector of solutions corrensdonded to times that was requested. It takes Vector of time points as a parameter and returns a vector of results

stormerVerlet2H

Arguments

:: (Applicative f, Num (f a), Show (f a), Fractional a)

=> a

Step size

-> (f a -> f a)

\(\frac{\partial H}{\partial q}\)

-> (f a -> f a)

\(\frac{\partial H}{\partial p}\)

-> V2 (f a)

Current \((p, q)\) as a 2-dimensional vector

-> V2 (f a)

New \((p, q)\) as a 2-dimensional vector

Störmer-Verlet integration scheme for systems of the form \(\mathbb{H}(p,q) = T(p) + V(q)\)

type Integrator a

Arguments

 = Double

Step

-> a

Initial value

-> a

Next value

Integrator function - Phi [h] |-> y_0 -> y_1