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Added an RK8 integration method #17

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7892fed
Added an RK8 integration method
jared711 Apr 3, 2020
dff5f91
Added RK8 type
jared711 Apr 3, 2020
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25 changes: 25 additions & 0 deletions src/integration.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -24,6 +24,31 @@ function discrete_dynamics(::Type{RK4}, model::AbstractModel, x::SVector, u::SVe
x + (k1 + 4k2 + 4k3 + k4)/6
end

function discrete_dynamics(::Type{RK8}, model::AbstractModel, y::SVector{N,T}, u::SVector{M,T},t, dt::T) where {N,M,T}
α = @SVector [ 2/27, 1/9, 1/6, 5/12, .5, 5/6, 1/6, 2/3, 1/3, 1, 0, 1 ];
β = @SMatrix [ 2/27 0 0 0 0 0 0 0 0 0 0 0 0;
1/36 1/12 0 0 0 0 0 0 0 0 0 0 0;
1/24 0 1/8 0 0 0 0 0 0 0 0 0 0;
5/12 0 -25/16 25/16 0 0 0 0 0 0 0 0 0;
.05 0 0 .25 .2 0 0 0 0 0 0 0 0;
-25/108 0 0 125/108 -65/27 125/54 0 0 0 0 0 0 0;
31/300 0 0 0 61/225 -2/9 13/900 0 0 0 0 0 0;
2 0 0 -53/6 704/45 -107/9 67/90 3 0 0 0 0 0;
-91/108 0 0 23/108 -976/135 311/54 -19/60 17/6 -1/12 0 0 0 0;
2383/4100 0 0 -341/164 4496/1025 -301/82 2133/4100 45/82 45/164 18/41 0 0 0;
3/205 0 0 0 0 -6/41 -3/205 -3/41 3/41 6/41 0 0 0;
-1777/4100 0 0 -341/164 4496/1025 -289/82 2193/4100 51/82 33/164 12/41 0 1 0]
χ = @SVector[0, 0, 0, 0, 0, 34/105, 9/35, 9/35, 9/280, 9/280, 0, 41/840, 41/840 ]; # Difference between two bottom layers of butcher tableau

f = y*zeros(eltype(y),1,13)

f[:,1] = dynamics(model,y,u,t)
for j = 1:12
f[:,j+1] = dynamics(model, y + dt*f*β[j,:],u,t + α[j]*dt)
end
return y + dt*f*χ
end


############################################################################################
# EXPLICIT METHODS #
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9 changes: 6 additions & 3 deletions src/model.jl
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Expand Up @@ -62,13 +62,16 @@ abstract type Implicit <: QuadratureRule end
"Integration rules of the form x′ = f(x,u,x′,u′), where x′,u′ are the states and controls at the next time step."
abstract type Explicit <: QuadratureRule end

"Fourth-order Runge-Kutta method with zero-order-old on the controls"
"Eigth-order Runge-Kutta method"
abstract type RK8 <: Implicit end

"Fourth-order Runge-Kutta method with zero-order-hold on the controls"
abstract type RK4 <: Implicit end

"Second-order Runge-Kutta method with zero-order-old on the controls"
"Second-order Runge-Kutta method with zero-order-hold on the controls"
abstract type RK3 <: Implicit end

"Second-order Runge-Kutta method with zero-order-old on the controls"
"Second-order Runge-Kutta method with zero-order-hold on the controls"
abstract type RK2 <: Implicit end

"Third-order Runge-Kutta method with first-order-hold on the controls"
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