Solving PDEs with mixed derivatives

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?

[Torsten]

I doubt that by a coordinate transformation, you can establish the form

dT'/dt' = a*d^2T'/dx'^2 + b*dT'/dx' + c

that would be needed to apply pdepe since your equation has a hyperbolic part (d^2T/dt*dx).

But what do you suggest ?

[Matthew Hunt]

Just use

and look for the condition where there is no mixed derivatives.

[Torsten]

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.

Answer 1

[Swaraj]

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!!