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.
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.