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RE: Re: PDE

• To: mathgroup at smc.vnet.net
• Subject: [mg35328] RE: [mg35297] Re: PDE
• From: "DrBob" <majort at cox-internet.com>
• Date: Mon, 8 Jul 2002 03:19:56 -0400 (EDT)
• Reply-to: <drbob at bigfoot.com>
• Sender: owner-wri-mathgroup at wolfram.com

The sign of your eigenvalues is wrong:

f = Sin[k x]*Sin[m y];
D[f, x, x] + D[f, y, y] // Factor

(-(k^2 + m^2))*Sin[k*x]*Sin[m*y]

Bobby

-----Original Message-----
From: Jens-Peer Kuska [mailto:kuska at informatik.uni-leipzig.de] 
To: mathgroup at smc.vnet.net
Subject: [mg35328] [mg35297] Re: PDE

Hi,

no but ist is easy by hand -- use the eigenfunctions

Sin[k Pi x/L]*Sin[m Pi y/L] 

and the eigenvalues 

k^2 Pi^2/L^2 + m^2 Pi^2/L^2

and use the Fourier series. That's the simplest example
in standard text books about PDE's. You don't need a 
computer algebra
for that.

Regards
  Jens

mitja Lakner wrote:
> 
> Is there any package for solving eigenvalue problem for the Laplacian
operator
> on the 2D (not rectangular) region with zero boundary value?
> 
> f_{xx}+f_{yy}= t f
> 
> Mitja Lakner