# Next\_step! resulting in slightly different results for the same inputs

**URL:** <https://discourse.julialang.org/t/next-step-resulting-in-slightly-different-results-for-the-same-inputs/119683>\
**Category:** Modelling & Simulations\
**Created:** [September 21, 2024, 8:27pm UTC](https://discourse.julialang.org/t/next-step-resulting-in-slightly-different-results-for-the-same-inputs/119683 "2024-09-21T20:27:01Z")\
**Posts on this page:** 1\
**Showing post:** 9

<div class="post-metadata">

**Author:** ![ufechner7](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ufechner7/32/51363_2.png) [@ufechner7](https://discourse.julialang.org/u/ufechner7)\
**Post date:** [September 22, 2024, 7:44pm UTC](https://discourse.julialang.org/t/next-step-resulting-in-slightly-different-results-for-the-same-inputs/119683/9 "2024-09-22T19:44:44Z")

</div>

I used the example [Tethers.jl/src/Tether\_07.jl at main · ufechner7/Tethers.jl · GitHub](https://github.com/ufechner7/Tethers.jl/blob/main/src/Tether_07.jl) and added `using Sundials`.

Getting the following results for tol = 1e-6:

- CVODE\_BDF()  
Elapsed time: 0.001612388 s, speed: 6202.0 times real-time  
Number of evaluations per step: 1.7
- QNDF(autodiff=true)  
Elapsed time: 0.00189734 s, speed: 5271.0 times real-time  
Number of evaluations per step: 2.2

@Bart_van_de_Lint So you are right, until now CVODE\_BDF() is the fastest solver, about 18% faster than the fastest Julia solver I found so far.

But less accurate… I mean, there is always a trade-off, fast solution or robust and accurate solution. Your choice.

By the way, try:  
?QNDF() and  
?CVODE\_BDF()

Both of them have a lot of options.

@ChrisRackauckas Why don’t we have a Julia solver yet that is faster than CVODE\_BDF() ?

Related: [CVODE\_BDF outperforms Julia solvers for stiff system biology model?](https://discourse.julialang.org/t/cvode-bdf-outperforms-julia-solvers-for-stiff-system-biology-model/113936)

---

_[View the full topic](https://discourse.julialang.org/t/next-step-resulting-in-slightly-different-results-for-the-same-inputs/119683)._