Lax-Wendroff method for advection equation with periodic boundary condition

I'm trying to solve advection equation in with and periodic boundary conditions . My approach is as follow:

clc,clear

xmin=0;

xmax=1;

m=400;%space

t=0;

h=1/(m+1);

n=10/(0.95*h);%time steps

a=1;

dt=0.95*h/a;

x=xmin:h:xmax;

a1=a*dt/(h);

% ic

u0=cos(2*pi*x)+.2*cos(10*pi*x);

% plot(x,u0,'k*')

% hold on

u=u0;

un=u0;

% v = VideoWriter('newfile2.avi');

% open(v)

for j=1:n%time

%bc

% u(1)=u(m+1);

for i=2:m+1%space

un(i)=u(i)-(a1/2)*(u(i+1)-u(i-1))+0.5*(a1)^2*(u(i+1)-2*u(i)+u(i-1));

end

un(1)=un(m+1);

un(m+2)=un(2);

u=un;

t=t+dt;

%exact

y_e=(cos(2*pi*(x-t))+.2*cos(10*pi*(x-t)));

plot(x,y_e)

hold on

plot(x,u,'bo-','MarkerFaceColor','r')

hold off

title(sprintf('time=%1.3f',t))

shg

pause(dt)

% frame = getframe(gcf);

% writeVideo(v,frame);

end

% close(v)

error=abs(max(y_e-un))

The code is running well. However, I'm not getting desired order of accuracy. Your help will be appreciated.

Answer 1

[Alan Stevens]

If you make dt=0.1*h/a; instead of dt=0.95*h/a; your max error reduces to 0.0355.

[Moslem Uddin]

I'm talking about order of accuracy.

[Torsten]

We can't see where you varied the spatial and/or temporal resolution and calculated the convergence order.

Or what is your definition of "order of accuracy" ?