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how to output quantities involving time derivatives in pdepe

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pdeval only seems to output the solution and the spatial derivative of the solution via [~,dudx]=pdeval(m,x,sol(i,:,1),x). It seems it's no use putting dudt in as in [~,dudt]=pdeval(m,x,sol(i,:,1),x). How to output quantities involving time derivatives of the solution and the like?

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Torsten
Torsten on 13 Feb 2024
Edited: Torsten on 13 Feb 2024
You don't have access to the spatial discretization of pdepe, thus no access to the exact time derivatives. But if you choose the output vector t fine enough, you can use the usual finite difference quotient in time:
dersol_t(i,:) = (sol(i+1,:,1)-sol(i,:,1))/(t(i+1)-t(i))
Maybe "deval" also works - I'm not sure. You can test it.
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feynman feynman
feynman feynman on 13 Feb 2024
Edited: feynman feynman on 13 Feb 2024
thanks! dersol_t(i,:) = (sol(i+1,:,1)-sol(i,:,1))/(t(i+1)-t(i)) is what I thought of but I wish there were sth provided by matlab that is more accurate.
I have no idea how to make deval work for pdepe solutions since deval(~,sol,~) requires sol to be an ode solution struct out of ode23,45 etc. Maybe I can forge an ode struct by hand?
Torsten
Torsten on 13 Feb 2024
You can attain higher order accuracy if you use more accurate difference formulae than the simple Euler forward I suggested. I think "deval" can't do better - at least if the ode integrator with which the results were achieved is not known to "deval" by the sol structure.

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