# Looking to parallelize (not parametrize) the solution to a large and highly stiff ODE system

**URL:** <https://discourse.julialang.org/t/looking-to-parallelize-not-parametrize-the-solution-to-a-large-and-highly-stiff-ode-system/116727>\
**Category:** Julia at Scale\
**Tags:** multithreading, ode, differentialequation, sundials, parallel-computing\
**Created:** [July 7, 2024, 3:58pm UTC](https://discourse.julialang.org/t/looking-to-parallelize-not-parametrize-the-solution-to-a-large-and-highly-stiff-ode-system/116727 "2024-07-07T15:58:36Z")\
**Posts on this page:** 1\
**Showing post:** 3

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**Author:** ![balaji\_sriram](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/balaji_sriram/32/208000_2.png) [@balaji\_sriram](https://discourse.julialang.org/u/balaji_sriram)\
**Post date:** [July 8, 2024, 7:05am UTC](https://discourse.julialang.org/t/looking-to-parallelize-not-parametrize-the-solution-to-a-large-and-highly-stiff-ode-system/116727/3 "2024-07-08T07:05:40Z")

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I have already tried using expoential solvers from ExponentialUtilities.jl , KrylovKit.jl and even solvers such as Exprb32 and 43 from DifferentialEquations.jl package for a miniature version of the original problem.  
**Here is a detailed reference to the same:** [Trying to solve a large system of highly stiff differential equations - #11 by balaji\_sriram](https://discourse.julialang.org/t/trying-to-solve-a-large-system-of-highly-stiff-differential-equations/114728/11).

They are horribly slow in my case (and sometimes are highly inaccurate over a large time period- see the note in the next paragraph). Ive also tried various other stiff solvers previously (such as Rodas, Kencarp, Rosenbrock etc.), but found CVODE\_BDF to be by far the most stable, accurate and fast solver of all. Since CVODE works well for my case, I would like to employ parallel processing (in my HPC) to these solvers (preferably). Also my HPC doesn’t have GPUs so at the moment I might not be able to explore the same.

**A quick note of the system:** The max values in the jacobian are of the order 1e12, the minimum nonzero values are 1e3 and i want to solve the problem till a span of 1e-3 seconds (a large time-span considering the fastest dynamics (1e12 Hz)are 9 orders faster than the slowest dynamics).

Also @ChrisRackauckas, as you recommended I will try using solvers such as LinearExponential(), and other [State-Independent Solvers](https://docs.sciml.ai/DiffEqDocs/stable/solvers/nonautonomous_linear_ode/#State-Independent-Solvers) and let you know the results soon.

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