# Symplectic integrators

**URL:** <https://discourse.julialang.org/t/symplectic-integrators/29056>\
**Category:** General Usage\
**Tags:** question\
**Created:** [September 23, 2019, 4:54am UTC](https://discourse.julialang.org/t/symplectic-integrators/29056 "2019-09-23T04:54:03Z")\
**Posts on this page:** 3\
**Page:** 1

<div class="post-metadata">

**Author:** ![bojohnson02](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/bojohnson02/32/9345_2.png) [@bojohnson02](https://discourse.julialang.org/u/bojohnson02)\
**Post date:** [September 23, 2019, 4:54am UTC](https://discourse.julialang.org/t/symplectic-integrators/29056/1 "2019-09-23T04:54:03Z")

</div>

In DifferentialEquations do the symplectic integrators require separable Hamiltonians? I’ve tried using a couple algorithms like Yoshida6 or KahanLi6 with a non-separable system and haven’t gotten good results when comparing them to just integrating the equations of motion from Hamilton’s equations.

---

<div class="post-metadata">

**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 23, 2019, 10:18am UTC](https://discourse.julialang.org/t/symplectic-integrators/29056/2 "2019-09-23T10:18:27Z")

</div>

They don’t necessarily require separable, but there are limitations mentioned in:

[http://docs.juliadiffeq.org/latest/solvers/dynamical\_solve.html#Dynamical,-Hamiltonian,-and-2nd-Order-ODE-Solvers-1](http://docs.juliadiffeq.org/latest/solvers/dynamical_solve.html#Dynamical,-Hamiltonian,-and-2nd-Order-ODE-Solvers-1)

FWIW, symplectic integrators only have an advantage in long time integrations.

---

<div class="post-metadata">

**Author:** ![bojohnson02](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/bojohnson02/32/9345_2.png) [@bojohnson02](https://discourse.julialang.org/u/bojohnson02)\
**Post date:** [September 23, 2019, 2:25pm UTC](https://discourse.julialang.org/t/symplectic-integrators/29056/3 "2019-09-23T14:25:31Z")

</div>

Got it, thanks for pointing out those limitations.