Help to adapt the resolution of an ODE in Matlab to Julia

Hello guys. I’m having trouble adapting a Matlab code that resolves a second-order ODE to the Julia equivalent.

This is the code in Matlab. It plots a graph with 3 curves:

syms y(x);
dy = diff(y);
edo = diff(y,x,2) == -0.1 * dy - 0.8 * y;
Bound_1 = y(0) == 5e-3;
Bound_2 = dy(0) == 0;
conds = [Bound_1 Bound_2];
t = [0, 30];
ySol(x) = dsolve(edo, conds);
fplot(ySol, t)
hold on
fplot(diff(ySol), t)
fplot(diff(ySol,2), t)
hold off

This is my equivalent Julia version. However, the resulting graph has only two curves.

f2(du, u, p, t) = -0.1du - 0.8u
u₀ = 5e-3
du₀ = 0.0
t = (0.0, 30.0)
prob = SecondOrderODEProblem(f2, du₀, u₀, t)
sol = solve(prob)

How do I make the u'' curve appear in the graph generated by the julia?

If you decrease the tolerances do they become the same?

The graph is correct but the curve representing the second order derivative is missing.


To interpolate the second-order derivative, you can use this:

ts = LinRange(t[1], t[2], 200)
z = sol(ts, Val{0})
dz = sol(ts, Val{1})

using Plots 
plot!(ts, dz[1,:])

# or 
plot(ts, [z[2,:] z[1,:] dz[1,:]] )

The sol(...) syntax is used for interpolation, see Solution Handling · DifferentialEquations.jl
and the Val{1} indicates that we want the first derivative of the solution.

Since you have a second-order problem, the solution vector has the form z = (u', u) and accordingly we have z' = (u'', u'). Therefore we get dz[1,:] ~ u''.