# A system of PDE and ODE

**URL:** <https://discourse.julialang.org/t/a-system-of-pde-and-ode/100290>\
**Category:** General Usage\
**Tags:** question\
**Created:** [June 13, 2023, 5:12pm UTC](https://discourse.julialang.org/t/a-system-of-pde-and-ode/100290 "2023-06-13T17:12:19Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![Reza\_AO](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/reza_ao/32/51137_2.png) [@Reza\_AO](https://discourse.julialang.org/u/Reza_AO)\
**Post date:** [June 13, 2023, 5:12pm UTC](https://discourse.julialang.org/t/a-system-of-pde-and-ode/100290/1 "2023-06-13T17:12:19Z")

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Is PINN capable of solving a time dependent system consisting of a PDE and an ODE?  
for example if there is a system like below:

> eq = [A \* Dt(u1(t,x)) ~ B \* Dx(u(t,x)) - C\* Dt(u2(t)),  
> Dt(u2(t)) ~ D \* u2(t) \* exp(E \* u1(t,x))]

For this system would PINN couple solve it or should I put it in iterations and put the u1 and u2 from previous steps into the equation for every new steps?

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**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:** [June 13, 2023, 11:22pm UTC](https://discourse.julialang.org/t/a-system-of-pde-and-ode/100290/2 "2023-06-13T23:22:47Z")

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> [@Reza\_AO](#):
>
> Is PINN capable of solving a time dependent system consisting of a PDE and an ODE?

Yup. It may not be as easy to solve as NNODE, which specializes the boundary condition in a nice way, but an ODE is just a 1-dimensional PDE so yeah it’s fine.