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Is Mathematica able to rearrange systems of PDEs (NOT solve them)?

Posted 10 years ago

Hello,

I'm trying to achieve the following: I want to use Mathematica to rearrange and resolve a system of PDEs, but I don't want it to give me an analytical or numerical solution. My example would be to do the Falkner-Skan transformation in Mathematica, meaning I have a set of PDEs (Navier-Stokes-eqn), and some "replacements" for the variables, and want the system to be transformed into another one. I can do it on paper, but it's a lot of writing and the potential to make error is really high. So I would prefer to do it with Mathematica, especially since I plan to transform more difficult systems later.

Essentially this process: Falkner Skan Derivation

The final result would be equation (128) in the document, an equation that contains only f and its derivatives, when the given input to Mathematica are definitions of f, eta, psi, etc.

Is this possible?

POSTED BY: Lennart M
2 Replies
Posted 10 years ago

Then what would be the right way of telling Mathematica what I want? I tried to input my equations e.g. like this

eqn={D[u[x,y],x]+D[v[x,y],y]==0,eta[x,y]==Sqrt[ue/(nu*x)]*y,psi==Sqrt[ue*nu*x]*f
[eta[x,y]],u[x,y]==D[psi[x,y],y],v[x,y]==-D[psi[x,y],x]}
FullSimplify[eqn]

Thus specifying which functions I have, and what their parameters are (u is a function of x and y, f is a function of eta, eta is a function of x and y again, ...) and then using FullSimplify, or Eliminiate[eqn, {x,y}] to get rid of the variables I don't want, but nothing happened, so I guess this is the wrong approach.

POSTED BY: Lennart M

I've only glanced at the Falkner Skan Derivation that you attached, but I'd say that if you can do it on paper, you can program it (and probably more generally) in Mathematica. I'd advise working through the derivation that you posted step-by-step in Mathematica and then proceed to generalize what you discover in one or more functions. it will probably be non-trivial, but doable.

POSTED BY: David Reiss
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