# Non linear time dependent problem
**URL:** https://community.freefem.org/t/non-linear-time-dependent-problem/856
**Category:** General Discussion
**Created:** [March 16, 2021, 6:39pm UTC](https://community.freefem.org/t/non-linear-time-dependent-problem/856 "2021-03-16T18:39:59Z")
**Posts on this page:** 14
**Page:** 1
### Author:  [@Laurent](https://community.freefem.org/u/Laurent)
#### Post date: [March 16, 2021, 6:39pm UTC](https://community.freefem.org/t/non-linear-time-dependent-problem/856/1 "2021-03-16T18:39:59Z")
Dear all,
I looking for an or more examples of nonlinear time dependent problem using Newton method or other.
Regards
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### Author:  [@frederichecht](https://community.freefem.org/u/frederichecht)
#### Post date: [March 17, 2021, 4:21pm UTC](https://community.freefem.org/t/non-linear-time-dependent-problem/856/2 "2021-03-17T16:21:58Z")
During the freefem days and all during teaching sessions, I solve of Boussinessq Equation
(Inccompressible Navier Stokes with temperature) to see Rayleigh-Bernard instability.
The Non linear Part is done with Fixe-Point and Newton iteration method,
And I use BDF 3 schema for the time integration.
[Rayleigh-Benard-time.edp](https://community.freefem.org/uploads/short-url/7wQywbkMyb4Wwdsve9S4CalfMZa.edp) (3.9 KB)
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### Author:  [@xiaojiemo](https://community.freefem.org/u/xiaojiemo)
#### Post date: [October 4, 2021, 1:54am UTC](https://community.freefem.org/t/non-linear-time-dependent-problem/856/3 "2021-10-04T01:54:06Z")
if i can have documentation for the PDE equations in this example ?
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### Author:  [@ligax](https://community.freefem.org/u/ligax)
#### Post date: [October 11, 2021, 12:43am UTC](https://community.freefem.org/t/non-linear-time-dependent-problem/856/4 "2021-10-11T00:43:04Z")
Would you please add the video link or slides here？ Thanks!
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### Author:  [@D\_N\_Sarkar](https://community.freefem.org/u/D_N_Sarkar)
#### Post date: [October 11, 2021, 4:18pm UTC](https://community.freefem.org/t/non-linear-time-dependent-problem/856/5 "2021-10-11T16:18:55Z")
I have a question with respect to “BDF 3 schema for the time integration”.
Can you please elaborate more on this time integration scheme? What is the order of accuracy of this time integration scheme?
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### Author:  [@xiaojiemo](https://community.freefem.org/u/xiaojiemo)
#### Post date: [October 13, 2021, 11:49am UTC](https://community.freefem.org/t/non-linear-time-dependent-problem/856/6 "2021-10-13T11:49:06Z")
have you get through the weak form derivation? I have been in this part weveral days and still haven’t get the same form as in FixePB.
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### Author:  [@frederichecht](https://community.freefem.org/u/frederichecht)
#### Post date: [October 29, 2021, 4:49pm UTC](https://community.freefem.org/t/non-linear-time-dependent-problem/856/7 "2021-10-29T16:49:38Z")
remark, on BDF3 schema to get the correct error leve (o(dt^3) l, you must initialize with schema of order
o(dt^2) because you have no sum for initialization so no problem init BDF1 for the fist set and BDF2 for the second step, and after BF3 , but if you want to go to BDF4 it will be wrong…
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### Author:  [@D\_N\_Sarkar](https://community.freefem.org/u/D_N_Sarkar)
#### Post date: [January 17, 2022, 6:26pm UTC](https://community.freefem.org/t/non-linear-time-dependent-problem/856/8 "2022-01-17T18:26:33Z")
Thank you for sharing the code.
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### Author:  [@D\_N\_Sarkar](https://community.freefem.org/u/D_N_Sarkar)
#### Post date: [February 1, 2022, 5:32am UTC](https://community.freefem.org/t/non-linear-time-dependent-problem/856/9 "2022-02-01T05:32:35Z")
The code is a serial code. Is there a parallel version of the code available?
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### Author:  [@frederichecht](https://community.freefem.org/u/frederichecht)
#### Post date: [February 1, 2022, 10:50am UTC](https://community.freefem.org/t/non-linear-time-dependent-problem/856/10 "2022-02-01T10:50:22Z")
They are no good parallel version to day.
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### Author:  [@qingYang](https://community.freefem.org/u/qingYang)
#### Post date: [March 23, 2024, 11:52pm UTC](https://community.freefem.org/t/non-linear-time-dependent-problem/856/11 "2024-03-23T23:52:28Z")
May I ask if anyone can download the second PDF from the manuscript, it shows that it cannot be opened
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### Author:  [@qingYang](https://community.freefem.org/u/qingYang)
#### Post date: [April 15, 2024, 1:41pm UTC](https://community.freefem.org/t/non-linear-time-dependent-problem/856/12 "2024-04-15T13:41:36Z")
Hello, have you solved the weak form problem later?
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### Author:  [@frederichecht](https://community.freefem.org/u/frederichecht)
#### Post date: [April 16, 2024, 2:27pm UTC](https://community.freefem.org/t/non-linear-time-dependent-problem/856/13 "2024-04-16T14:27:27Z")
No, I do nothing on this problem
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### Author:  [@qingYang](https://community.freefem.org/u/qingYang)
#### Post date: [April 21, 2024, 2:05am UTC](https://community.freefem.org/t/non-linear-time-dependent-problem/856/14 "2024-04-21T02:05:53Z")
Thank you, professor. I have another question.
In the program you contributed, the (u · ▽ T) part ,the u and T are both defined in a same fluid domain. If I want to define u in the local fluid domain and T in the global domain, how should I solve this problem? I have tried indirect coupling, first calculating u and then calculating T, but I couldn’t get the result I wanted.