Re: elliptic equation solved with 2 boundaries
- To: mathgroup at smc.vnet.net
- Subject: [mg43380] Re: [mg43294] elliptic equation solved with 2 boundaries
- From: Selwyn Hollis <selwynh at earthlink.net>
- Date: Wed, 27 Aug 2003 04:05:06 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
I'm saying that the function you have there does NOT satisfy Laplace's
equation. To wit:
f[x_, y_] = x^2 + y^2 + (x^2 + y^2 - 1)*(x^2 -
4)*(y^2 - 4)*(0.0969 + 0.0521*(x + y) - 0.0673*(x^2 +
y^2) - 0.0474*x*y + 0.0131*(x^3 + y^3) + 0.0186*(x^2*y + x*y^2));
D[f[x, y], x, x] + D[f[x, y], y, y] //Simplify
0.0262*x^7 + x^6*(-0.1346 + 0.11159999999999999*y) +
0.9306*x^5*(-1.7928004028673246 + y)*
(1.487191118534636 + y) + 1.1919999999999997*x^4*
(-3.029757574452006 + y)*(-1.6752088537259546 + y)*
(1.6561409248222545 + y) + 1.1920000000000002*x^3*
(-2.2228390629540007 + y)*(-1.4449671507956403 + y)*
(0.19453320678744204 + y)*(1.8826689801165617 + y) +
0.9306*x^2*(-3.408858946401705 + y)*
(-2.4293086236257073 + y)*(-1.414388472070547 + y)*
(1.1851701370865004 + y)*(2.162163467874128 + y) +
0.0262*(-10.686298999992214 + y)*(-2.887058280512249 +
y)*(-1.7433406794998176 + y)*(-1.2281602713350044 +
y)*(0.7051004253831695 + y)*(1.4173203071348504 + y)*
(9.285032918668596 + y) + 0.11159999999999999*x*
(-5.803866761388662 + y)*(-1.5368142970813419 + y)*
(1.4155876360966493 + y)*(5.0496910616106625 + y)*
(0.9111394041260903 - 1.672984736011502*y + y^2)
That doesn't look like zero to me.
Perhaps f satisfies some other elliptic equation that you forgot to
mention?
-----
Selwyn Hollis
http://www.math.armstrong.edu/faculty/hollis
On Tuesday, August 26, 2003, at 09:20 AM, Ferdinand.Cap wrote:
> Hi,
> Thank you for your interest in my notebook. The LAPLACE
> equation has complex characteristics and is therfor called an elliptic
> partial differential eqatiuon. The theory of boundary value problems
> (Table 1.1. on page 14 in the book mentioned in the notebook )shows
> that an elliptic partial differential equation can only satify one
> boundary
> value probblem. My notebokk demonstrates that under special conditions
> also 2 boundary value problems can be satisfied - run the notebook!
> Due to the approoximation method -variational calculus - the LAPLACIAN
> is
> not zero, but numerically small F.C
>
> Selwyn Hollis wrote:
>
>> CAP F,
>>
>> What elliptic equation is this function suppose to solve? It's
>> Laplacian is definitely not zero.
>>
>> -----
>> Selwyn Hollis
>> http://www.math.armstrong.edu/faculty/hollis
>>
>> On Saturday, August 23, 2003, at 08:09 AM, CAP F wrote:
>>
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