Lax-Wendroff solve hyperbolic equations

zyf

I'm trying to solve a standard hyperbolic equations with lax-wendroff method, but after two thousand timesteps, got divergence result. I'm not sure if the BC manipulation is right.

du/dt+a*dv/dz=0

dv/dt+a*du/dz=0

with a=5000.here 'u' is velocity, 'v' is stress. t:[0,nt] z:[0,nz]

set B.C.:at point z=0, u=0

at point z=nz, v=0

I.C.: u=0;v=0;except at point uz=nz/2, u=1.

difference with Lax-Wendroff method. because 'a=5000', so set 'dt/dz=1e-4' to stablize L-W method.

at boudnary set

u(-1,t)=-u(1,t)

v(-1,t)=2*v(0,t)-v(1,t)

u(nz+1,t)=2*u(nz,t)-u(nz-1,t)

v(nz+1,t)=-v(nz-1,t)

does the boudnary setting right?

thanks . Zyf