# Integrating large systems of ODEs

**URL:** <https://discourse.julialang.org/t/integrating-large-systems-of-odes/132428>\
**Category:** Modelling & Simulations\
**Created:** [September 16, 2025, 7:18am UTC](https://discourse.julialang.org/t/integrating-large-systems-of-odes/132428 "2025-09-16T07:18:16Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![PersiaJK](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/persiajk/32/213262_2.png) [@PersiaJK](https://discourse.julialang.org/u/PersiaJK)\
**Post date:** [September 16, 2025, 7:18am UTC](https://discourse.julialang.org/t/integrating-large-systems-of-odes/132428/1 "2025-09-16T07:18:16Z")

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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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**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [September 16, 2025, 8:08am UTC](https://discourse.julialang.org/t/integrating-large-systems-of-odes/132428/2 "2025-09-16T08:08:25Z")

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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.