Stability of numerical method for 1D Burger's equation

I am trying to solve 1D viscous Burger's equation numerically and I cannot apply von Neumann analysis because the equation is non-linear. How do I predict the stability criteria for my system? I also need to predict the criteria when its inviscid(which basically makes it non-linear advection equation).

The FD schemes that I am using are 1st order FT for time, 1st order BS for the advection term and 2nd order CS for diffusion term. Though I know there are better FD schemes, I still want to analyze stability of this scheme.

Update
Forgot to include initial and boundary condition. Everything is so meaningless without it..
The domain of flow is between -2<=x<=8
Initial conditions are such that 1<=u<=2 for the entire flow domain
Boundary conditions define constant positive velocity at left and right boundaries.

• I'm not sure what you mean by FT, BS, and CS. I suppose these are low-order forward, backward, and centered differences? Oct 10 '13 at 5:49
• Sorry about that..FT stands for forward in time...BS means backward in space....these are from upwind method and CS stands for central in space...I am trying to convey the FD approximations that I used for each derivative.. Oct 10 '13 at 7:06
• A good reference is Randy LeVeque's book on hyperbolic equations Oct 10 '13 at 19:52

In the inviscid case, it's well known (and follows from the reasoning above) that this scheme is stable for CFL number $\le 1$.