Re: reaction diffusion equation !

• To: mathgroup at smc.vnet.net
• Subject: [mg87337] Re: [mg87186] reaction diffusion equation !
• From: "Nabeel Butt" <nabeel.butt at gmail.com>
• Date: Tue, 8 Apr 2008 05:35:48 -0400 (EDT)
• References: <200804031017.FAA26076@smc.vnet.net>

```Hi Khaled,
Your problem is a non-linear variant of the classic fisher
equations.There are local  fixed-point schemes that can guarantee
convergence but global solutions cannot be guaranteed to exist.
(i) I have used Mathematica to work out the steady state solution and in
that case you just eliminate the derivative in t and it becomes a standard
laplace equation.
(ii) I highly doubt that this kind of problem would have travelling wave
solution because in Poincare phase plane only one critical point exists.
In such scenarios you would need to use a "finite-difference" scheme
that achieves stable results.Since,Mathematica does have "finite-difference"
notebooks available check those out over the web.
Best of luck!
Nabeel

On Thu, Apr 3, 2008 at 6:17 AM, khaled sayed <k_s_mahmoud at hotmail.com>
wrote:

> Dear sir
> Can NDSolve in Mathematica solves the nonlinear reaction diffusion
> equation in two dimensions
> (Tt-Uxx-Uyy=f(U) with Drichlit B.C.). I ask u kindly to send me the
> mathematica program solves the transient heat equation in two dimension  or
> the heat diffusion equation if u already have it.
> Thanks in advance for help and cooperation
> regards
> khaled sayed
> Khaled Sayed Mahmoud Ibrahim Department of MathematicsFaculty of
> ScienceHelwan University Helwan, Cairo, EgyptTel.: (+20)18-25-35-272
> Fax: (+20)-2-25588-586k_s_mahmoud at hotmail.com
>
>

--
"We have not succeeded in answering all our problems.The answers we have
found only serve to raise a whole set of new questions.In some ways we feel
that we are as confused as ever,but we believe we are confused on a higher
level and about more important things."

Nabeel Butt
UWO,London