% Showing solution of Utt - c Uxx =0 that has initial zero velocity 


x=-8:0.05:8;
t=-8:0.05:8;

[X,T]=meshgrid(x,t);

set(gca,'FontSize',[16]);
figure(1)

c = 0.5;

Z1=exp(-(X-c*T).^2/2);
Z2=exp(-(X+c*T).^2/2);
Z=Z1+Z2;

surfl(X,T,Z);
shading interp
colormap(gray)
ylabel('t')
xlabel('x')
zlabel('u(x,t)')
view([15 52])
axis tight

steps=4;
N=length(t(1:steps:length(t)));
xM=max(max(x));
xm=min(min(x));
M=max(max(Z));
m=0;

figure(2)
clf

fprintf('Press any key to continue\n')
i=1;
plot(x,Z(i*steps+1,:),'LineWidth',2)
axis([xm xM 0 M])

pause
set(gca,'FontSize',[16]);
for i=0:N-1
 plot(x,Z(i*steps+1,:),'LineWidth',2)
 axis([xm xM 0 M])
 pause(0.01)
end

steps=1;
N=length(t(1:steps:length(t)));

figure(3)
clf
i0=(N+1)/2;
plot(x,Z(i0*steps+1,:),'LineWidth',2)
axis([xm xM 0 M])

fprintf('Press any key to continue\n')
pause

set(gca,'FontSize',[16]);
for i=i0:N-1
 plot(x,Z(i*steps+1,:),x,2*Z2(i*steps+1,:),x,2*Z1(i*steps+1,:),'r','LineWidth',2)
 axis([xm xM 0 M])
 pause(0.01)
end