# Numerical Lax-Wendroff scheme order of convergence on Burgers equation

I was suggested to move that question here.

The question to be as follows.

### Statement of the problem

Is it possible to achieve the second order of convergence (OOC) of Lax-Wendroff (LxW) scheme applied to solve inviscid Burgers equations with discontinuous initial data?

If no, then how to achieve (and prove numerically) OOC of 2nd order (of LxW scheme) in quasilinear problem?

### Wolfram Mathematica code

(*Initial data*)
u0[x_] := 1 - UnitStep[x - 0.1];
Flux[u_] := 0.5 u^2;
u = u0[xTbl];
dt = Abs[\[Sigma]] /Abs[Max[u]] dx;
un = 0*u;
F = Flux[u];

(*LW*)
t = 0;
While[t < tFin,
(*Main loop*)
un[[2 ;; nx - 1]] = u[[2 ;; nx - 1]] -
0.50 \[Sigma] (F[[3 ;; nx]] - F[[1 ;; nx - 2]]) +
0.25 \[Sigma]^2 ((u[[3 ;; nx]] + u[[2 ;; nx - 1]]) (F[[3 ;; nx]] -
F[[2 ;; nx - 1]]) - (u[[2 ;; nx - 1]] +
u[[1 ;; nx - 2]]) (F[[2 ;; nx - 1]] - F[[1 ;; nx - 2]]));
(*BC*)
un[] = u[];
un[[nx]] = u[[nx]];
(*Update*)
u = un;
F = Flux[u];
nstep = nstep + 1;
t = t + dt
];


### Output

nx = {50, 100, 200, 400, 800};
L1err = {0.0217352, 0.0107321, 0.00533915, 0.00207726, 0.00132978};
p = {1.0181, 1.00725, 1.36192, 0.643502}


Average OOC equals

1.00769