Tsit5() and DP5() stability

New to Julia
,
1

Hi guys,

I am wrapping up a script to solve the TOV equation, similar to the TOVsolver_Julia, and I used ‘CommonSolve’ and ‘DifferentialEquations’ packages. In the solver, unlike the case in TOVsolver_Julia, I used callbacks to terminate the integration when P<0

    condition(u, t, integrator) = u[1] < 0
    affect!(integrator) = terminate!(integrator)
    cb = DiscreteCallback(condition, affect!)

and applied Tsit5 and DP5 (the same as TOVsolver_Julia). However, I found some unsmooth results that did not occur in my hand-crafted RK4 method in the mass-radius curves for different initial conditions for the density at r=0,

Using solve in CommonSolve

Screenshot 2026-05-15 at 10.54.24
Screenshot 2026-05-15 at 10.54.24603×402 23 KB

In addition, I found out that in some cases, the integration becomes unstable, and a warning pops up for both Tsit5 and DP5 algorithms.

> Warning: Verbosity toggle: dt_epsilon 
> │  At t= 9656.595735553243, dt was forced below floating point epsilon 1.8189894035458565e-12. Aborting. There is either an error in your model specification or the true solution is unstable (or the true solution can not be represented in the precision of Float64.
> └ @ SciMLBase ~/.julia/packages/SciMLBase/TKP6E/src/integrator_interface.jl:736

Does anyone know if there is a better approach for this type of differential equation?

2

Can you try ContinuousCallback instead? It can hit within the integration step, so it should be more stable

3

Thanks, just tried ContinuousCallback and also switched the callback off for another test. The same warning occurs.