2.7.4 Stability Exercises
Download the MATLAB® code in Section 2.7.2. Modify this code to compute the eigenvalues of the FTBS method with periodic boundary conditions. For CFL=1, where are there eigenvalues of \(A\)?
To implement a backward spatial discretization, we modify the matrix A:
for i = 2:Nx-1 A(i,i) = u/dx; A(i,i-1) = -u/dx; end
Compute analytically the eigenvalues for the FTBS method with periodic boundary conditions. The eigenvalues are