# Resolve an hyperbolic system with FF++

**URL:** <https://community.freefem.org/t/resolve-an-hyperbolic-system-with-ff/3047>\
**Category:** General Discussion\
**Created:** [March 17, 2024, 4:27pm UTC](https://community.freefem.org/t/resolve-an-hyperbolic-system-with-ff/3047 "2024-03-17T16:27:50Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![Gigi](https://avatars.discourse-cdn.com/v4/letter/g/a587f6/32.png) [@Gigi](https://community.freefem.org/u/Gigi)\
**Post date:** [March 17, 2024, 4:27pm UTC](https://community.freefem.org/t/resolve-an-hyperbolic-system-with-ff/3047/1 "2024-03-17T16:27:50Z")

</div>

Hi,  
please, how we cal write with FF++, the variational formulation of the following hyperbolic system:

\tau\*\dfrac{\partial q}{\partial t}= -q - D\* \dfrac{\partial V}{\partial x},

\dfrac{\partial V}{\partial t}=- \dfrac{\partial q}{\partial x} -\sigma\*V

where the uknown functions are V(x,t) and q(x,t), D, \tau, \sigma and b are constant.

Thank you in advance

---

<div class="post-metadata">

**Author:** ![fb77](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/fb77/32/3796_2.png) [@fb77](https://community.freefem.org/u/fb77)\
**Post date:** [March 18, 2024, 12:32pm UTC](https://community.freefem.org/t/resolve-an-hyperbolic-system-with-ff/3047/2 "2024-03-18T12:32:49Z")

</div>

You can use an implicit scheme in time or a Crank-Nicholson time scheme as follows

 ![maxwell](https://canada1.discourse-cdn.com/flex030/uploads/freefem/original/2X/0/03878499a686d2f65af3851b416e9ab1aa79e3b5.jpeg)

You can use `P2` for `q` and `V`. You multiply (5) by a test function in `P2` to get `q`,  
and multiply (3) by a test function in `P2` to get `V`.