# Time dependent non linear problem

**URL:** <https://community.freefem.org/t/time-dependent-non-linear-problem/1623>\
**Category:** General Discussion\
**Created:** [March 24, 2022, 4:05pm UTC](https://community.freefem.org/t/time-dependent-non-linear-problem/1623 "2022-03-24T16:05:38Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![jeremie](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/jeremie/32/1063_2.png) [@jeremie](https://community.freefem.org/u/jeremie)\
**Post date:** [March 24, 2022, 4:05pm UTC](https://community.freefem.org/t/time-dependent-non-linear-problem/1623/1 "2022-03-24T16:05:38Z")

</div>

Hello,

In FreeFEM, is it possible to deal with a time dependent non linear problem like this one :

```auto
\nabla^2 A = - \sigma(dA/dt) * dA/dt

```

with sigma, a non linear function.

I saw that I must use a `uold` variable for the time-dependent part, and `uu` for the non linear part, but how can I mix both of them. Should I create a `uuold` maybe ?

Thank you in advance,

Best regards,

Jeremie

---

<div class="post-metadata">

**Author:** ![frederichecht](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/frederichecht/32/15_2.png) [@frederichecht](https://community.freefem.org/u/frederichecht)\
**Post date:** [March 24, 2022, 4:42pm UTC](https://community.freefem.org/t/time-dependent-non-linear-problem/1623/2 "2022-03-24T16:42:10Z")

</div>

The only problem is to write de scheme in time and prove the scheme is stable and convergente.

After than no real problem on idea is

make a Fixed point also with 3 value  
A, Ap, Al

```auto
Ap = A; // previous value
for (iter = ...
    Al = A 
   \nabla^2 A = - \sigma((Al-Ap)/dt) * (A-Ap)/dt
   if( ||Al-A|| < eps) break

```