DAE Solvers

DAE Solvers

Recomended Methods

For medium to low accuracy DAEs in mass matrix form, the Rodas4 and Rodas42 methods are good choices which will get good efficiency. The OrdinaryDiffEq.jl methods are also the only methods which allow for Julia-defined number types. For high accuracy (error <1e-7) on problems of Vector{Float64} defined in mass matrix form, radau is an efficient method.

If the problem cannot be defined in mass matrix form, the recommended method for performance is IDA from the Sundials.jl package if you are solving problems with Float64. It's a very well-optimized method, and allows you to have a little bit of control over the linear solver to better tailor it to your problem. A similar algorithm is daskr. Which one is more efficient is problem-dependent.

Full List of Methods

OrdinaryDiffEq.jl

These methods require the DAE to be an ODEProblem in mass matrix form. For extra options for the solvers, see the ODE solver page.

Rosenbrock Methods

SDIRK Methods

SDIRK Methods

Sundials.jl

Note that the constructors for the Sundials algorithms take a main argument:

Example:

IDA() # Newton + Dense solver
IDA(linear_solver=:Band,jac_upper=3,jac_lower=3) # Banded solver with nonzero diagonals 3 up and 3 down
IDA(linear_solver=:BCG) # Biconjugate gradient method                                   

All of the additional options are available. The constructor is:

IDA(;linear_solver=:Dense,jac_upper=0,jac_lower=0,krylov_dim=0,
    max_order = 5,
    max_error_test_failures = 7,
    max_nonlinear_iters = 3,
    nonlinear_convergence_coefficient = 0.33,
    nonlinear_convergence_coefficient_ic = 0.0033,
    max_num_steps_ic = 5,
    max_num_jacs_ic = 4,
    max_num_iters_ic = 10,
    max_num_backs_ic = 100,
    use_linesearch_ic = true,
    max_convergence_failures = 10)

See the Sundials manual for details on the additional options.

DASKR.jl

DASKR.jl is not automatically included by DifferentialEquations.jl. To use this algorithm, you will need to install and use the package:

Pkg.add("DASKR")
using DASKR

DASSL.jl

ODEInterfaceDiffEq.jl