Solver for differential algebraic equations with arbitrary implicit Runge Kutta method


As the title suggest, is there any package in Julia that enables solving differential algebraic equations DAEs with arbitrary implicit Runge Kutta (beyond the available ones) methods? Alternatively, is there any publicly available implementation that does that? All I found was the Julia solvers that have their default methods and error controls.

If you look here there are a couple of them DAE Solvers · DifferentialEquations.jl . If you search for radau you will find some that are specifically runge kutta.

Thanks a lot. But the choices are limited. What if I want to use a method that is not listed there?

If you want to add a new solver the dev docs have a nice tutorial Home · SciML Developer Documentation

If you don’t want to add the new solver yourself, you could file an issue to request the method be considered for implementation. However, open source software relies on contributions from interested parties, so I would suggest trying to implement the new solver.

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It’s worth noting that you almost never want to actually solve DAEs. Instead, it’s almost always better to convert to mass matrix form.

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Doing so from the tableau is really bad, so you have to manually transform into a separate form to reduce the LU cost.