[cinclus]

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