Toddy,

I would start with thinking about the time discretization scheme you want
to use and in particular which terms you want to treat explicitly and which
implicitly.
After you have done that, you might still end up with a nonlinear problem
in which case you should have a look at
https://www.dealii.org/current/doxygen/deal.II/step_15.html and
https://www.dealii.org/current/doxygen/deal.II/step_25.html.

Best,
Daniel

Am Mi., 25. Aug. 2021 um 09:11 Uhr schrieb Toddy Liu <[email protected]
>:

> Dear Deal.II community,
>
> I'm getting trouble in constructing system matrix of a complex PDE. My PDE
> is a time-dependent equation, and in simplicity it seems like
>
> [image: screenshot.png]
> U is the variable, t denotes the time. D, alpha, beta are constant. So
> could you please give me some advice about doing this or any reference in
> existing dealii examples.
>
> Thank you very much.
>
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