Boundary value problem with NDSolve

• To: mathgroup at smc.vnet.net
• Subject: [mg27414] Boundary value problem with NDSolve
• From: "ronehwa" <ronehwa.eo85g at nctu.edu.tw>
• Date: Sun, 25 Feb 2001 00:53:37 -0500 (EST)
• Organization: NCTU-CC
• Sender: owner-wri-mathgroup at wolfram.com

```Hi Dear All,
Consider the Following question:

eq1=D[f[z,t],t]+v D[f[z,t],z]
eq2=D[g[z,t],t]-v D[g[z,t],z]
twowave=NDSolve[ { eq1 == 0,eq2 == 0,
f[z,0] == z+0.32*132/(1-0.32^2), g[z,0]
== -z+132/(1-0.32^2),
f[0,t] == 0.32*g[0,t], 0.32*f[100,t] ==
g[100,t] },
{f,g},{z,0,100},{t,0,80}] ;

eq1==0 represents f[z,t] is a right-going propagation wave,
and eq2==0 represents g[z,t] is a left propagation wave.
v is the propagation velocity.
At the boundary z=100, the right-going wave refects 32% its amount and turn
left to propagate,
At the boundary z=0, the left-going wave also refects 32% its amount and
turn right to propagate.

After executing twowave, the mathematica 4.0 return the following message:
"NDSolve::"bcart": "Warning: An insufficient number of boundary conditions
have been specified. Artificial boundary effects may be present in the
solution."
I think the key to the question should be the boundary condition. How can I
set the the boundary condition properly?