DifferentialEquations.jl
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Adding support for 2nd order index-3 DAE using HHT
It would be nice to be able to solve index-3 DAE type problems without index reduction. This article, and a few others, show the use of HHT (Hilber, Hughes, Taylor) as an extension to \alpha-based Newmark methods as a potential solution to this class of problem. It does also add numerical damping that might be advantageous in some mechanical applications with non-physical high frequency due to numerical discretization.
This is also another article that touches on such methods.
@SebastianM-C maybe we could fit this in?