Finite difference schemes and Partial differential equations, Strikwerda, 2ed, p.22
$$u_t+\frac 1 3(t-2)u_x + \frac 2 3 (t+1) w_x +\frac 1 3 u = 0$$ $$w_t + \frac 1 3 (t+1)u_x + \frac 1 3 (2t-1) w_x - \frac 1 3 w =0 $$ for $x \in [-3,3], t \in [0,2]$. The initial values are $u(0,x)=\max(0,1-|x|), w(0,x)=\max(0,1-2|x|)$ and boundary values are $u=0$ and $w_x=0$. Solve the system in the form given; do not attempt to diagonalize it.
I numerically solved the problem using Lax-Friedrichs scheme, and I want to compare my numerical solution with the analytic solution. So how can I solve the problem? Also is it impossible to solve it by diagonalization? (I don't know why the last sentence in the problem is given.)
