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MathGroup Archive 1999

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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



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