Is a PDE with (∂P/∂x)² term linear or nonlinear?

Ein Krieger · Mar 14, 2013

hello, guys
Below is the equation I am concerned with:

Partial differential equation: ∂p/∂t = (k/(cφμ)) (c[(∂p/∂x)²] + ∂²p/∂x²), with the (∂p/∂x)² term inside the bracket.

Is the above equation non-linear because of (delta P/delta x)^2 term assuming other variables are constant and don't change with pressure , P?

HallsofIvy · Mar 14, 2013

It is non-linear because of, as you say, that [itex]\left[\partial p/\partial x\right]^2[/itex]

Ein Krieger · Mar 14, 2013

Ok.
What kind of method can you suggest to deal with [∂p/∂x] 2 ?

I am going to convert the above equation to ODE by method of lines in Matlab. I guess that non-linear terms require special approach.

Is a PDE with (∂P/∂x)² term linear or nonlinear?

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