Instability after reducing number of equations in DifferentialEquations.jl

General Usage
1

I have a large set of differential equations (O(10000)) which I try to solve using Tsit5() and DifferentialEquations.jl.

sol = solve(
prob,
Tsit5(),
dtmax = 0.1,
maxiters = 100000,
progress = true,
saveat = 0.01,
)

I found a symmetry in the system, which allowed me to reduce the amount of equations. However, after some time, the symmetrized set of equations becomes unstable (see screenshot). Before that the dynamics looks the same as in the non-symmetrized case.

I do not understand this behavior - is the redundancy making the equations more stable?

I tried choosing alg_hints = :auto to automatically choose a solver, but the execution time became very large and the instabilities remained.

comparison
comparison700×500 19.9 KB

2

You can try the most accurate solvers(I like radauIIA5 but rosenbrock are also great) if that fails then you can try Sundial Fortran ones and if this fail too, it’s the model that may have something weird going one.

3

Did you try to set abstol and reltol to a low value, e.g. 1e-6?

4

Thanks for the quick reply! My equations are complex, and the solvers you suggested only work with real equations as far as I can see…
Do you think it is worthwile to restructure my code such that I propagate real and imaginary part separately?

5

Thanks for the quick reply! I set them 1e-6 but the instability is still there…

6

how is Rodas5(autodiff=false) doing ? maybe later on for performance you can split depends on the solver you will need

7

It gets stuck at the beginning… Maybe there are too many equations?

8

Can you share the equations? This will be impossible to debug at a distance.