Theres a good (if slightly out of date) comparison between the features for ODE solving, putting DifferentialEquations.jl against the suites commonly used in other langauges: http://www.stochasticlifestyle.com/comparison-differential-e... (linked in the blog as well)
The problem is that mexjulia is the established package for those bindings, but it needs an update for newer versions of MATLAB (https://github.com/twadleigh/mexjulia/issues/58) which won't happen because the author moved on (https://github.com/twadleigh/mexjulia#mexjulia-embedding-jul...). If anyone is willing to put time into building/maintaining the binding libraries I'd be willing to use them. The issue is that, for any non-OSS language, the essential tooling (CI, benchmarking, accessibility) are absent, making it hard to maintain bindings for.
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[ 4.0 ms ] story [ 14.4 ms ] threadWorth checking out.
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Edit: Nevermind, its not out of date
I'd be curious to see if there is any progress on the matlab interoperability as well (my field is mostly matlab).