Add discretization method from d/dt

[schillic]

This requires JuliaReach/LazySets.jl#2800.

using ReachabilityAnalysis, Plots
using ReachabilityAnalysis: ForwardDdt
import DifferentialEquations

A = [0.0 1.0; -1.0 0.0]
X0 = BallInf([1.0, 1.0], 0.1)

prob = @ivp(x' = Ax, x(0) ∈ X0)
dt = (0.0, 20.0)

δ = 2e-1
X1 = linear_map(exp(A*δ), X0)
template = PolarDirections(200)

sol = solve(prob, ensemble=true, include_vertices=true, trajectories=0, tspan=dt, alg=LGG09(δ=δ, template=template, approx_model=ForwardDdt()));
sol_ua = solve(prob, tspan=dt, alg=LGG09(δ=δ, template=template, approx_model=ForwardDdt(oa=false)));

plot(X0)
plot!(X1)
plot!(sol[1], vars=(1, 2), alpha=0.2)
plot!(convex_hull(X0, X1), alpha=0.2)
plot!(sol_ua[1], vars=(1, 2), alpha=0.5)
plot!(ensemble(sol), vars=(1, 2), alpha=1, c=:black)
xlims!(-ρ([-1.0, 0.0], sol[1]), ρ([1.0, 0.0], sol[1]))
ylims!(-ρ([0.0, -1.0], sol[1]), ρ([0.0, 1.0], sol[1]))

plot(sol[1:9], vars=(1, 2), alpha=0.2)
plot!(sol_ua[1:9], vars=(1, 2), alpha=0.5)
plot!(ensemble(sol), vars=(1, 2), alpha=1, c=:black)
xlims!(1, 1.6)