t_0 = 0;
t_f = 1;
N = 128;
M = 100;

[u1,err,x,t1] = heat1(t_0,t_f,M,N);
figure(1)
for j=0:20
     plot(x,u1(:,j+1),'.-')
     title(t1(j+1),'FontSize',16)
     xlabel('Explicit Euler','FontSize',16)
     pause(1)
end

figure(2)
plot(t1,log10(max(abs(u1))))
title('log10(maximum of u) versus time','FontSize',16)
xlabel('notice that things start to grow exponentially shortly before time 0.2')

display('hit any key for more')
pause

figure(1)
for j=0:20
   [k,amp] = find_spec(u1(1:N,j+1));
   plot(k,amp,'.-')
     axis([0,N/2,-17,2])
     pause(1)
end

display('hit any key for more')
pause

[u2,err,x,t1] = heat3(t_0,t_f,M,N);
figure(1)
for j=0:20
     plot(x,u2(:,j+1),'.-')
     title(t1(j+1),'FontSize',16)
     xlabel('Fully implicit','FontSize',16)
     pause(1)
end

figure(2)
plot(t1,log10(max(abs(u2))))
title('log10(maximum of u) versus time','FontSize',16)

display('hit any key for more')
pause

figure(1)
for j=0:20
   [k,amp] = find_spec(u2(1:N,j+1));
   plot(k,amp,'.-')
     axis([0,N/2,-17,2])
     pause(1)
end

display('hit any key for more')
pause

[u3,err,x,t1] = heat_cn(t_0,t_f,M,N);
figure(1)
for j=0:20
     plot(x,u3(:,j+1),'.-')
     title(t1(j+1),'FontSize',16)
     xlabel('Fully implicit','FontSize',16)
     pause(1)
end

figure(2)
plot(t1,log10(max(abs(u3))))
title('log10(maximum of u) versus time','FontSize',16)

display('hit any key for more')
pause

figure(1)
for j=0:20
   [k,amp] = find_spec(u3(1:N,j+1));
   plot(k,amp,'.-')
     axis([0,N/2,-17,2])
     pause(1)
end