Re: Programing Differential Equations in Fipy

Hi Zhiwen,

Hope all is well.

On Mon, Jul 7, 2008 at 4:44 PM, Zhiwen Liang <liangz@...> wrote:
> Hi all,
>
> Professor Garcia and I are working on solving some differential equations
> that look different from those that can be assembled by the regular Fipy
> terms. It would be great if you can give us some ideas.
>
> First, we are dealing with terms that are cross differentials with respect
> to different axis. For example, \frac{ \partial^2 \phi }{\partial x \partial
> y}.
>
> Second, the variables that are being solved for are embedded in several
> equations. For example, we want to solve these two equations: (Sorry they
> are not good examples.)
> \frac{\partial^2 \phi_1}{\partial x^2}+\frac{\partial^2 \phi_2}{\partial
> y^2}=0
> \frac{\partial^2 \phi_1}{\partial x \partial y}+\frac{\partial^2
> \phi_2}{\partial x \partial y}=0

We now have anisotropic diffusion, which, I think, deals with the
terms above. For example,

    \frac{\partial^2 \phi_1}{\partial x \partial y}

can be represented by,