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