Is it possible to introduce time dependent function in any of the coefficient of pde form used in pde toolbox?

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Hello,
I am trying to solve sine gordon equation with a dissipiation term using pde toolbox. I need to introduce partial derivative of u with respect to 't' and a function which is dependent on 't' where 't' stands for time. I tried to put all of them in coefficient 'f' using diff(u,t) but it doesn't work. Is there any way I can introduce them in the equaition?

Accepted Answer

MD AZIZ AR RAHMAN
MD AZIZ AR RAHMAN on 29 Jul 2020
I solved this problem by using pde solver (pdepe) instead of pde toolbox. I needed to convert the sine gordon equation with du/dt term into a system of two pde as belows:
u1_t=u2
u2_t=u1_xx-sin(u1)+a*u2
and solved for both u1 and u2.

More Answers (1)

Alan Weiss
Alan Weiss on 20 Jul 2020
Edited: Alan Weiss on 20 Jul 2020
This portion of the documentation describes how to set up a general PDE for solution by PDE Toolbox. This is the general workflow. You can specify coefficients as described, for example, here. Yes, coefficients can depend on time.
I do not know the Sine-Gordon equation with dissipation. The basic Sine-Gordon equation is a 1-D equation that is easy to put into the form required by the toolbox
You woud use , , , .
I suppose that you would use a 2-D model with constant values in one (essentially unused) dimension. But maybe I am wrong and this is not so easy to put into 2-D.
Good luck,
Alan Weiss
MATLAB mathematical toolbox documentation
  1 Comment
MD AZIZ AR RAHMAN
MD AZIZ AR RAHMAN on 26 Jul 2020
I was in need of both non zero m and d. I didn't understand in the manual regarding what to do with d when m is nonzero.

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