Outgoing wave boundary conditions with NDSolve
- To: mathgroup at smc.vnet.net
- Subject: [mg15874] Outgoing wave boundary conditions with NDSolve
- From: Keith Watt <kwatt at astro.umd.edu>
- Date: Wed, 17 Feb 1999 23:33:31 -0500
- Organization: University of Maryland Astronomy
- Sender: owner-wri-mathgroup at wolfram.com
Hello -
I'm trying to use NDSolve on a wave equation with outgoing wave
(Sommerfeld) boundary conditions. I can set up the equation (with
initial and boundary comditions) if I use fixed or periodic boundary
condtions, but not with outgoing wave. The outgoing wave BCs are:
Derivative[0,1][y][L,t]+Derivative[1,0][y][L,t] == 0
and
Derivative[0,1][y][-L,t]+Derivative[1,0][y][-L,t] == 0
where L is the length of the string that is carrying the waves.
Here is my input:
sol1
=NDSolve[{eq,ic1,ic2,Derivative[0,1][y][L,t]==-Derivative[1,0][y][L,t],
Derivative[0,1][y][-L,t]==-Derivative[1,0][y][-L,t]}/.L->100,
y[x,t],{x,-L,L}/.L->100,{t,0,100},MaxStepSize->10,MaxSteps->100000]
where ic1 and ic2 are equations defining initial conditions.
Mathematica responds with:
Part::"partw":
"Part 3 of {<< 1 >>} does not exist."
and
NDSolve::"ndnum":
"The right-hand side of the differential equation does not evaluate
to a
number at t == 0."
What is the proper way to input these boundary conditions?
Many thanks..
Keith Watt
kwatt at astro.umd.edu