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MathGroup Archive 2004

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Need your help to solve a PDE.

  • To: mathgroup at smc.vnet.net
  • Subject: [mg52824] Need your help to solve a PDE.
  • From: "Satya Das" <satyaranjandas77 at yahoo.com>
  • Date: Tue, 14 Dec 2004 05:59:14 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Hi All,
    I need to solve an equation. It would be a great help if you solve this.
The problem is mentioned at
http://www.geocities.com/satyaranjandas77/PDE.pdf. I had to go this way
because I was not able to send an attachment.

I had made many attempts myself, but since it is more than 5 years I am out
of college I need to relearn how to solve PDE. :(
Is it possible to solve this equation using mathmatica? Even the power
series solution will work just fine for me.

Thanks in advance,
satya

--- Below are some more related info ----

I did try Phi(r, theta) = F(r)G(theta), but this did not work.
I had tried the followings too:
Phi(r, theta) = (1/r) Psi(r, theta) -> to reduce the equation to look more
like solvable.
Phi(r, theta) = Psi(r sin(theta)/r_0, theta) -> to make the equation
dimensionless, and from the equation it seems like r sin(theta) is more
natural.
Phi(r, theta) = Psi(r_0 sin(theta)/r, theta) -> here r and r_0 have changed
their position.

I did not try power series because the equation is in two variables.
Boundary condition is that Phi vanishes as r->oo.
Other condition on Phi is that it is symmetric about theta = pi/2 => Phi(r,
theta) = Phi(r, pi - theta).

I even tried a trial function:
Phi(r, theta) = (r /(r_0^2 sin^2 theta)) (1 - exp(-r^2/(r_0^2 sin^2
theta))), but this does not satisfy the equation.

You may ignore my attempts because I am not too sure if I was doing the
right thing.
I realized that my mathematical capabilities have been deteriorated during
last five years.

Thanks,
satya



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