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