Hello all,
I am trying to solve a differential equation with interval coefficients using the packages “IntervalArithmetic.jl” and “ReachabilityAnalysis.jl” in Pluto.jl notebook. When I tried to plot the solution I got this plot
I wish to get a complete blue color plot (10 seconds), but I am getting it for less than 2 seconds. Could you please let me know what is the problem and how can I resolve it?
I used the code shown below-
begin
@taylorize function f(du, u, p, t)
du[1] = ( u[1] + u[2] ) * ( u[1] - u[3] ) * ( u[1] + u[4] )
#encode uncertain params
du[2] = zero(u[1]) # p[1]
du[3] = zero(u[1]) # p[2]
du[4] = zero(u[1]) # p[3]
end
p_int = (1.0..1.0) × (2.0..2.01) × (3.0..3.0)
U0 = Singleton([1.0]) × convert(Hyperrectangle, p_int)
prob = @ivp(u' = f(u), dim: 4, u(0) ∈ U0);
sol = solve(prob, tspan=(0.0, 10.0), TMJets(abstol=1e-5));
solz = overapproximate(sol, Zonotope);
function g(du, u, p, t)
a, b, c = p
n = 1
du[1] = ( u[1] + a ) * ( u[1] - b ) * ( u[1] + c)
end
u0 = [1.0] # initial conditions
p = (1.0, 2.0, 3.0) # unperturbed parameter values
tspan = (0.0, 10.0) # time span to solve the system over
prob = ODEProblem(g, u0, tspan, p)
sol = solve(prob)
#plot
plot(solz, vars=(0, 1), lw=0.3)
plot!(sol, vars=(0, 1), legend=false, ylabel="x(t)", xlabel="Time")
savefig("Julia_plot.png")
end