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Solving PDEs with mixed derivatives

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Matthew Hunt
Matthew Hunt 2023-1-10
回答： Swaraj 2023-4-6
Suppose I have an equation of the form:
Can I use pdepe to solve that equation as is, or do I have to do a co-ordinate transformation first to get rid of the mixed derivative?
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Matthew Hunt
Matthew Hunt 2023-1-10
Just use
and look for the condition where there is no mixed derivatives.
Torsten
Torsten 2023-1-11
编辑：Torsten 2023-1-11
And what do you get as PDE after applying the transformation ?
Is it of the form
dT'/dt' = a*d^2T'/dx'^2 + b*dT'/dx' + c
solvable for pdepe ?
If yes: you can apply pdepe, if no: not.

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回答（1 个）

Swaraj
Swaraj 2023-4-6
Hi,
I understand you want to use “pdepe” to solve PDE with mixed derivatives.
“pdepe” is normally used to solve 1-D parabolic and elliptic PDEs and not for mixed derivatives.
I would suggest you to go through the below documentation to understand when to use “pdepe” for solving PDE’s.
Solve 1-D parabolic and elliptic PDEs - MATLAB pdepe (mathworks.com)
I hope it helps.
Thanks!!

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