how to output quantities involving time derivatives in pdepe

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feynman feynman 2024-2-13

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评论： Torsten 2024-2-13

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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Answer 1

Torsten 2024-2-13

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编辑：Torsten 2024-2-13

在 MATLAB Online 中打开

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.

https://uk.mathworks.com/help/matlab/ref/deval.html

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feynman feynman 2024-2-13

编辑：feynman feynman 2024-2-13

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 2024-2-13

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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