Rodas4 vs Rodas4P vs Rodas4P2 solvers

Today I found that the solver Rodas4P2 is working best for my model. For an tolerance of 1e-7 it is 4 times faster than Simulink, operating at a tolerance of 1e-3.

But what is the difference between Rodas4, Rodas4P and Rodas4P2?

I know that Rodas is described in literature, but I could not find any paper explaining Rodas4P or Rodas4P2… Is there any paper about it?

There’s Improvement of Rosenbrock-Wanner Method RODASP | SpringerLink and Construction of Rosenbrock–Wanner method Rodas5P and numerical benchmarks within the Julia Differential Equations package - BIT Numerical Mathematics which is about Rodas5P Note that you might want to try using Rodas5P which is very similar to Rodas4P but higher order.

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Thanks a lot! Rodas5P is indeed even faster, but at some point I saw that it had stability problems when using a step input…

If you’re using a step input, you should probably be using tstops or a ContinuousCallback to tell the solver where the discontinuity is (see Handling Instability When Solving ODE Problems).

Just tested to add tstops. It works, but it is not sufficient to add a tstop at the time of the discontinuity, but I need one more for a perfect result. Example (assuming the step happens at 200s):

function simulate(sys, ω, ω0, U, U0, D; p = [ U => U0 ], prn=true, duration=1000)
    u0  = [ω    => ω0,  # this is a fixed initial value
           D(ω) => 0.0] # the value for the derivative is an inital estimate

    # simulation parameters
    tspan = (0.0, duration)
    dt = 0.01
    ts = 0:dt:duration

    # run the simulation
    prob = ODEProblem(sys, u0, tspan, p)
    sol = solve(prob, Rodas5(), tstops=[200, 200+dt], saveat=ts)

This works perfect. Thank you!

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Is it the same bug as reported here?

I don’t know, looks like it, but I did not report that and a different solver was used…