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? Please help me solve this problem, I will deeply appreciate your help. ronehwa.