DAE Solvers

Recomended Methods

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.

If your problem requires special Julia types like arbitrary precision numbers, then dassl is the method of choice.

Special Keyword Arguments

Implemented Solvers

Sundials.jl

• IDA - This is the IDA method from the Sundials.jl package.

Note that the constructors for the Sundials algorithms take an argument:

• linearsolver - This is the linear solver which is used in the Newton iterations. The choices are:

  • :Dense - A dense linear solver

  • :Band - A solver specialized for banded Jacobians. If used, you must set the position of the upper and lower non-zero diagonals via jac_upper and jac_lower.

  • :Diagonal - This method is specialized for diagonal Jacobians.

  • BCG - A Biconjugate gradient method.

  • TFQMR - A TFQMR method.

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                                   

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

• daskr - This is a wrapper for the well-known DASKR algorithm.

DASSL.jl

• dassl - A native Julia implementation of the DASSL algorithm.