       Re: Solution for coupled PDE via Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg31317] Re: Solution for coupled PDE via Mathematica
• From: "Alan Mason" <swt at austin.rr.com>
• Date: Sat, 27 Oct 2001 01:08:35 -0400 (EDT)
• References: <9rb7fm\$5kg\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hello Jun.
I think can can pretty much forget about using NDSolve to solve your
problem.  Mathematica does not claim that it can solve PDE's very well, let
alone systems of PDE's.  Solving PDE's numerically is very difficult and
success depends crucially on the particular form of the PDE.  Even at the
theoretical level solutions may fail to exist, or may be nonunique.  You
can't just write down a system of PDE's and expect to find a solution even
in principle, unless you have some good physical motivation for the
equations in the first place.

I suggest you look at books on numerical approximation that cover PDE's
(most do not in any depth).  An old but still  good choice here is
"Numerical Solution of PDEs in Science and Engineering" by L. Lapidus and G.
Pinder, which discusses various finite difference approximations for a
variety of PDE's.  If you want to use Mathematica, you can translate that
code into Mathematica without too much difficulty.  The hard part is
modifying the code to suit your application; this will require some
specialized knowledge and ingenuity on your part, nobody else can do this
for you.  You don't state what your equations are.  If they are three
first-order, linear equations then finding a solution shouldn't be too hard,
provided the problem is well-posed.

A good reason for using Mathematica is its excellent multiprecision
computing capability.  By setting \$MinPrecision to 32, say, you can get quad
precision and Mathematica keeps track of the actual precision.  This is very
helpful in analyzing error propagation, stability, mesh dependence, etc.
For production runs you should probably use C++ code if running time is a
factor.

Alan

"Jun Lin" <jl_03824 at yahoo.com> wrote in message
news:9rb7fm\$5kg\$1 at smc.vnet.net...
> Does anybody know how to use NDSolve to find a specific solution of a
> set of three coupled Partial Differencial Equations (PDE)? Any help
> will be very appreciated.
>
> Jun Lin
>

```

• Prev by Date: Re: Re: Zero does not Equal Zero
• Next by Date: Re: SplineFit - Parametrization ?
• Previous by thread: Solution for coupled PDE via Mathematica