Lax Friedrich for square wave

Hello there! This is my first post here so I apologize if my introduction is not correct.

I'd like to ask clarifications concerning a Matlab code I wrote to analyze a square wave using Lax-Friedrich I do not understand why I have such big oscillations in the results, if not for too low value of Courant number

Thanks in advance!

%%Lax-Friedrich

a=0.5; %wave speed deltax=0.1; deltat=0.005; c=a*deltat/deltax; %courant number

X=-3:deltax:3; T=0:deltat:3;

%initial conditions u=zeros(length(X),1); i=find(X==-0.5); j=find(X==0.5); u(i:j)=1; un=[];

for t=T

[u]=laxfried(u,c); un=[un,u];

end

figure plot(X,un(:,1),'g') hold on plot(X,un(:,100),'b') plot(X,un(:,150),'r') plot(X,un(:,200),'m') plot(X,un(:,300),'k') plot(X,un(:,500),'k')

%%subroutine function

function [unew]=laxfried(u,c)

[m,n]=size(u); unew=zeros(m,n); for i=2:length(u)-1 unew(i)=-c*0.5*(u(i+1)-u(i-1))+0.5*(u(i+1)+u(i-1)); end