# PDEsim

## Synopsis

PDEsim is a Monte Carlo partial differential equation solver.
It's still in development, but is already able to put out some
nifty graphics.

## Sample Output

This should be the graph of the solution
$\Phi (x,y)$
to the elliptical partial differential equation
$(1+y)\frac{{\partial}^{2}\Phi}{\partial {x}^{2}}+2x\frac{{\partial}^{2}\Phi}{\partial x\partial y}+(1-y)\frac{{\partial}^{2}\Phi}{\partial {y}^{2}}-\frac{\partial \Phi}{\partial x}=0$
with boundary values given by
$f(x,y)=x+2y$
on the unit circle
${x}^{2}+{y}^{2}=1$ .

(That was in MathML; probably illegible to most everybody
right now...)

## The Algorithm

Short summary goes here.

## Development Roadmap

Currently, all of the parameters PDEsim needs (for
example, the actual equation it's solving) are compiled
in. Changing them is easy, but may require understand
both the algorithm and C programming; this rather limits
PDEsim's audience. Clearly, the next step for PDEsim is
adding the ability to read from the command line the
numerical parameters (easy) and the PDE to be solved (hard?).

Why the latter might be hard: Reading a PDE off
the command line first requires some description language
that works as text; it's hard to type in those partial
derivatives. (How does MATLAB handle this?) Also, the
random_walk() probabilities are dependent on the PDE;
it may be difficult to automate the conversion of PDE
coefficients into probabilities. Got to check...

## Getting The Source

If you'd like to get your hands dirty with C code,
you can browse the CVS repository on the PDEsim
project page,
hosted by Sourceforge.
I'm still working on it; I'd also welcome improvements from anyone
who wants to contribute. Compiling PDEsim requires the GNU
plotutils
package; specifically, the libplot library. Also available is
a fairly recent snapshot
that will compile even when the most recent version doesn't, and
doesn't require CVS to set up.

Mark Jeffcoat

jeffcoat@alumni.rice.edu

Last Updated October 15, 2000.