First-order PDE with side condition
- To: mathgroup at smc.vnet.net
- Subject: [mg120952] First-order PDE with side condition
- From: James <icorone at hotmail.com>
- Date: Thu, 18 Aug 2011 03:24:21 -0400 (EDT)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
Hi guys,
I'd like to check my analytic solution of the following PDE using NDSolve. The initial condition is a side-condition on the line y=ex/3 and I don't know how to set up NDSolve for that:
e^(-x)u_x+1/(y^2) u_y-e^(x) y u=0; u(x,ex/3)=e
Here's a start setting up NDSolve which I know is not correct. Maybe I need to use the method of lines and specify a temporal variable. Not sure and didn't see any examples for that in the PDE info for NDSolve. I'm hoping someone could help me fix it.
NDSolve[{Exp[-x]*D[u[x, y], x] + D[u[x, y], y]/
y^2 - Exp[x]*y*u[x, y] == 0,
u[x, (E*x)/3] == E}, u, {x, 0, 1}, {y, 0, 1}]
Thanks guys.