Integrating large systems of ODEs

Specific Domains Modelling & Simulations
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Hello! I am pretty new to Julia and I am looking for some answers and suggestions for a project of mine.
I am translating a code from C to Julia because I would like to divide the code in modules and possibly take advantage of libraries and packages. In my original code, I use Runge-Kutta to integrate a large system of ODEs:

\tau \frac{dr_i}{dt} = - r_i + \Phi(W^T \vec{r})

where i \in [N] and N = 10000 but W is sparse. I have been trying to understand what is the best package for integrating such a large number of equations, either DifferentialEquations.jl or NetworkDynamics.jl. Or maybe it is enough to copy and paste the RK4 method in Julia, like I did in the C version, which already took into account the sparsity (the loops are of order of the number of elements of W).

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RK4 isn’t tolerance controlled, and it has slow convergence, so I’d generally recommend folks just use DiffEq’s Tsit5 (can just directly using OrdinaryDiffEqTsit5 for just that one solver). NetworkDyamics.jl is a modeling library that builds ODEs for DifferentialEquations so whether it should be used is more of a modeling choice.

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