Solver choice

ODE solver choice

HetaSimulator.jl relies on the SciML solver ecosystem. Solvers can be used in HetaSimulator simulation and parameter estimation functions (sim, fit, etc.) via the alg keyword argument (for example, see sim). One can also set relative and absolute tolerances (reltol, abstol) and other stepsize-related settings via relevant keyword arguments. See DiffEqDocs for details.

If no solver is provided the default one AutoTsit5(Rosenbrock23()) will be used with reltol=1e-3 and abstol=1e-6 for simulation problems and reltol=1e-6 and abstol=1e-8 for parameters estimation.

Starting from OrdinaryDiffEq.jl v7, solvers are distributed through smaller subpackages. HetaSimulator.jl includes and reexports a focused set of these packages:

Package	Example solvers available after `using HetaSimulator`
`OrdinaryDiffEqTsit5`	`Tsit5()`, `AutoTsit5(...)`
`OrdinaryDiffEqRosenbrock`	`Rosenbrock23()`, `Rodas5P()`
`OrdinaryDiffEqBDF`	`FBDF()`, `QNDF()`
`OrdinaryDiffEqSDIRK`	`TRBDF2()`, `KenCarp4()`, `Kvaerno5()`

This means common nonstiff, stiff, BDF, Rosenbrock, and SDIRK methods can be used directly:

sol = sim(
    scen; 
    alg = Rodas5P(),
    reltol=1e-6,
    abstol=1e-8
)

To use a solver from another SciML package, add that package to your Julia environment and load it together with HetaSimulator. For example, Verner methods are provided by OrdinaryDiffEqVerner:

using Pkg
Pkg.add("OrdinaryDiffEqVerner")

using HetaSimulator
using OrdinaryDiffEqVerner

sol = sim(scen; alg = Vern7())

Similarly, SUNDIALS solvers such as CVODE_BDF() are provided by Sundials.jl:

using Pkg
Pkg.add("Sundials")

using HetaSimulator
using Sundials

sol = sim(scen; alg = CVODE_BDF())

For distributed simulations, load any additional solver package on all workers, for example with @everywhere using OrdinaryDiffEqVerner.

The following DiffEq Docs page provides general advice on how to choose a solver suitable for your ODE system. For many ODE systems the following simplified guideline is sufficient:

If your system is small (~10 ODEs) go with the default AutoTsit5(Rosenbrock23()) solver
If your system is medium-sized (~50 ODEs) choose Rodas5P()
If the system is large and stiff choose FBDF() or QNDF()
If FBDF() / QNDF() fails to solve the system check the model and try it again :)
If FBDF() / QNDF() still fails to solve the system or the integration takes too long try using CVODE_BDF() from Sundials.jl*.

*You should be cautious when using CVODE_BDF(). In many cases it is the fastest solver, however the accuracy of the solution is often the tradeoff. You shouldn't use it with tolerances higher than ~ reltol=1e-4 and abstol=1e-7.