[SciPy-Dev] Delay Differential Equation (DDE) solver

[Jansen Jérôme]

My dear SciPy community,

In my PhD, I work on biomechanical problematics which are (sometime)
modeled with delay differential equations.
Being an avid user of python and SciPy, I looked for DDEs solver but ... I
was surprised not to find it in SciPy. On the contrary, I discovered lots
of more or less old and very different projects about DDEs in Python
(JiTCDDE, ddeint, pydelay, diffeqpy). While in other programming languages,
robust code exist (matlab: dde23, julia: DelayDiffEq.jl, fortran: DKLAG6
...).
So I decided to start implementing a solver using the architecture of
scipy.integrate.solve_ivp.

The fork us here :
https://github.com/jrmejansen/scipy/tree/ddeSolver

I added the folder "*scipy/integrate/_dde*" and modified files from
"scipy/integrate/_ivp" to resolve DDEs. You would find also some benchmarks
but not yet unit tests.

At this time, the solver, *solve_dde*, handles DDEs with constant delays
for none stiff equations.

Does my code interest the SciPy community ?
If it does, I can add extensive unit tests and also docstring.

I am open to any discussion and do not hesitate to give me feedbacks.
Best regards,
Jérôme JANSEN.
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