Burgers equation with constant wave velocity:

∂u/∂t + c ∂u/∂x = ∂²u/∂x²

where c=1, v=0.1, 0

Initial condition: u(x,0)-sin(x); periodic boundary condition: u(0,t)-(2,) 

Questions: 

(1) Apply Fourier stability analysis to show its G factor.

2) Based on the G factor from Q1, if Δ = 0.01, choose a proper range of Ar and make sure the explicit difference equation is conditionally stable. 

(3) Choose Ar=0.01 and Δ=0.01, calculate the distribution of u(x) ∈ [0,2].

4) Now if we choose the wave speed c-u, please repeat Q1 to Q3.