Plotting Graph - 1D Advection

I have the following code and the plots are correct, but I am having trouble making the three separate plots with the correct title and legend, etc. How do I do this so it is correct for each separate figure?

clear all; clc; close all;      % clear workspace and editor and close figures, respectively
hold on

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

xlength = 2;                    % length of computational domain
n       = 1000;                 % number of grid points
h       = xlength / (n-1);      % dx 

cfl     = 0.9 ;                 % cfl = U dx/dt with stability between 0 and 1
U       = 1;                    % advective speed
dt      = h * cfl / U;          % dt - which is now function of cfl, h & dx
tout    = 1;                    % desired output time
time    = 0;                     

x       = zeros (1,n);          % initialising grid points
fn      = zeros (1,n);          % initialising solution of first-order Upwind scheme
fnlw    = zeros (1,n);          % initialising solution of Lax-Wendroff scheme
fnlf    = zeros (1,n);          % initialising solution of Lax-Friedrichs scheme
f       = zeros (1,n);          
flw     = zeros (1,n);                     
freal   = zeros (1,n);          
x(1)    = 0; 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

for time = [0 0.5 1] 
    z    = 0.75 * exp(-(((x-0.5)/0.1)).^2); 
    
for i = 2:n                     % making the mesh
    x(i)   = x(i-1) + h;
end

for i = 1:n
    f(i)   = 0.75 * exp(-(((x(i)-0.5)/0.1)).^2);  % first-order Upwind scheme
    flw(i) = 0.75 * exp(-(((x(i)-0.5)/0.1)).^2);  % Lax-Wendroff scheme
    flf(i) = 0.75 * exp(-(((x(i)-0.5)/0.1)).^2);  % Lax-Friedrichs scheme
end

nt = time/dt;

for k = 1:nt
    
for i = 2:n                      % first-order Upwind scheme
    flux   = U * (f(i)-f(i-1));
    fn(i)  = f(i)-(dt/h) * flux;
end
fn(1) = fn(n);                   % boundary condition for first-order Upwind scheme
f     = fn;                      % boundary condition for first-order Upwind scheme

for i = 2:n-1                    % Lax-Wendroff scheme
    l0       = (dt/(2*h)) * U *(flw(i+1)-flw(i-1));  
    h0       = (dt^2/(2*h^2)) * U.^2 * (flw(i+1)-(2*flw(i))+flw(i-1));
    fnlw(i)  = flw(i) - l0 + h0;
end
fnlw(1) = fn(n);                 % boundary condition for Lax-Wendroff scheme
fnlw(n) = fn(1);                 % boundary condition for Lax-Wendroff scheme
flw     = fnlw;                  % boundary condition for Lax-Wendroff scheme

for i = 2:n-1                    % Lax-Friedrichs scheme
    fnlf(i)  = 0.5 * (flf(i-1)+flf(i+1))-(dt/(2*h)) * U * (flf(i+1)-flf(i-1));
end
fnlf(1) = fn(n);                 % boundary condition for Lax-Friedrichs scheme
fnlf(n) = fn(1);                 % boundary condition for Lax-Friedrichs scheme
fnlf(i) = fn(i);                 % boundary condition for Lax-Friedrichs scheme
fnlf(n) = fnlf(1);               % boundary condition for Lax-Friedrichs scheme
flf     = fnlf;                  % boundary condition for Lax-Friedrichs scheme

time = nt*dt;
freal(:) = 0.75 * exp(-(((x(:)-0.5)/0.1)).^2);

for i = 2:n-1
    freal(i) = 0.75 * exp(-(((x(i)-0.5-U*time)/0.1)).^2);
end
freal(1) = freal(n);
freal(n) = freal(1);
end

figure(1)
plot (x,z,'b')                   % plot initial
hold on
plot (x,freal,'g')               % plot real
hold on
plot (x,f,'k')                   % plot Upwind
hold on

figure(2)
plot (x,z,'b')                   % plot initial 
hold on
plot (x,freal,'g')               % plot real
hold on
plot (x,flf,'r')                 % plot Lax-Friedrichs
hold on

figure(3)
plot (x,z,'b')                   % plot initial
hold on
plot (x,freal,'g')               % plot real 
hold on
plot (x,flw,'c')                 % plot Lax-Wendroff
hold on

title('\color{black}\fontsize{12}\bf Concentration Profile of Plume')
legend('Initial','Real','First-Order Upwind','Lax-Friedrichs','Lax-Wendroff')
set (gca, 'fontsize', 14)
xlabel('\color{black}\fontsize{12}\bf Displacement, x')
xlim([0,2])
ylabel('\color{black}\fontsize{12}\bf Concentration, c')

ErrFOUp = h * sqrt(sum((fn-freal).^2))   % error in first-order Upwind scheme
ErrLaxW = h * sqrt(sum((fnlw-freal).^2)) % error in Lax-Wendroff scheme
ErrLaxF = h * sqrt(sum((fnlf-freal).^2)) % error in Lax-Friedrichs scheme
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

[Rik]

Backup of this question:

Plotting Graph - 1D Advection

clear all; clc; close all;      % clear workspace and editor and close figures, respectively
hold on

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

xlength = 2;                    % length of computational domain
n       = 1000;                 % number of grid points
h       = xlength / (n-1);      % dx 

cfl     = 0.9 ;                 % cfl = U dx/dt with stability between 0 and 1
U       = 1;                    % advective speed
dt      = h * cfl / U;          % dt - which is now function of cfl, h & dx
tout    = 1;                    % desired output time
time    = 0;                     

x       = zeros (1,n);          % initialising grid points
fn      = zeros (1,n);          % initialising solution of first-order Upwind scheme
fnlw    = zeros (1,n);          % initialising solution of Lax-Wendroff scheme
fnlf    = zeros (1,n);          % initialising solution of Lax-Friedrichs scheme
f       = zeros (1,n);          
flw     = zeros (1,n);                     
freal   = zeros (1,n);          
x(1)    = 0; 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

for time = [0 0.5 1] 
    z    = 0.75 * exp(-(((x-0.5)/0.1)).^2); 
    
for i = 2:n                     % making the mesh
    x(i)   = x(i-1) + h;
end

for i = 1:n
    f(i)   = 0.75 * exp(-(((x(i)-0.5)/0.1)).^2);  % first-order Upwind scheme
    flw(i) = 0.75 * exp(-(((x(i)-0.5)/0.1)).^2);  % Lax-Wendroff scheme
    flf(i) = 0.75 * exp(-(((x(i)-0.5)/0.1)).^2);  % Lax-Friedrichs scheme
end

nt = time/dt;

for k = 1:nt
    
for i = 2:n                      % first-order Upwind scheme
    flux   = U * (f(i)-f(i-1));
    fn(i)  = f(i)-(dt/h) * flux;
end
fn(1) = fn(n);                   % boundary condition for first-order Upwind scheme
f     = fn;                      % boundary condition for first-order Upwind scheme

for i = 2:n-1                    % Lax-Wendroff scheme
    l0       = (dt/(2*h)) * U *(flw(i+1)-flw(i-1));  
    h0       = (dt^2/(2*h^2)) * U.^2 * (flw(i+1)-(2*flw(i))+flw(i-1));
    fnlw(i)  = flw(i) - l0 + h0;
end
fnlw(1) = fn(n);                 % boundary condition for Lax-Wendroff scheme
fnlw(n) = fn(1);                 % boundary condition for Lax-Wendroff scheme
flw     = fnlw;                  % boundary condition for Lax-Wendroff scheme

for i = 2:n-1                    % Lax-Friedrichs scheme
    fnlf(i)  = 0.5 * (flf(i-1)+flf(i+1))-(dt/(2*h)) * U * (flf(i+1)-flf(i-1));
end
fnlf(1) = fn(n);                 % boundary condition for Lax-Friedrichs scheme
fnlf(n) = fn(1);                 % boundary condition for Lax-Friedrichs scheme
fnlf(i) = fn(i);                 % boundary condition for Lax-Friedrichs scheme
fnlf(n) = fnlf(1);               % boundary condition for Lax-Friedrichs scheme
flf     = fnlf;                  % boundary condition for Lax-Friedrichs scheme

time = nt*dt;
freal(:) = 0.75 * exp(-(((x(:)-0.5)/0.1)).^2);

for i = 2:n-1
    freal(i) = 0.75 * exp(-(((x(i)-0.5-U*time)/0.1)).^2);
end
freal(1) = freal(n);
freal(n) = freal(1);
end

figure(1)
plot (x,z,'b')                   % plot initial
hold on
plot (x,freal,'g')               % plot real
hold on
plot (x,f,'k')                   % plot Upwind
hold on

figure(2)
plot (x,z,'b')                   % plot initial 
hold on
plot (x,freal,'g')               % plot real
hold on
plot (x,flf,'r')                 % plot Lax-Friedrichs
hold on

figure(3)
plot (x,z,'b')                   % plot initial
hold on
plot (x,freal,'g')               % plot real 
hold on
plot (x,flw,'c')                 % plot Lax-Wendroff
hold on

title('\color{black}\fontsize{12}\bf Concentration Profile of Plume')
legend('Initial','Real','First-Order Upwind','Lax-Friedrichs','Lax-Wendroff')
set (gca, 'fontsize', 14)
xlabel('\color{black}\fontsize{12}\bf Displacement, x')
xlim([0,2])
ylabel('\color{black}\fontsize{12}\bf Concentration, c')

ErrFOUp = h * sqrt(sum((fn-freal).^2))   % error in first-order Upwind scheme
ErrLaxW = h * sqrt(sum((fnlw-freal).^2)) % error in Lax-Wendroff scheme
ErrLaxF = h * sqrt(sum((fnlf-freal).^2)) % error in Lax-Friedrichs scheme
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Answer 1

[Sulaymon Eshkabilov]

Hi,

Here is the corrected part of your code and the rest of your code remains the same:

...

figure(1)
plot (x,z,'b')                   % plot initial
hold on
plot (x,freal,'gx')               % plot real
hold on
plot (x,f,'k')                   % plot Upwind
title('\color{black}\fontsize{12}\bf Fig 1 ???')  % Add a necessary title name
legend('Initial','Real','First-Order Upwind')
set (gca, 'fontsize', 14)
xlabel('\color{black}\fontsize{12}\bf Displacement, x')
xlim([0,2])
ylabel('\color{black}\fontsize{12}\bf Concentration, c')
hold off

figure(2)
plot (x,z,'b')                   % plot initial 
hold on
plot (x,freal,'gx')               % plot real
hold on
plot (x,flf,'r')                 % plot Lax-Friedrichs
title('\color{black}\fontsize{12}\bf Fig 2 ???')  % Add a necessary title name
legend('Initial','Real','Lax-Friedrichs')
set (gca, 'fontsize', 14)
xlabel('\color{black}\fontsize{12}\bf Displacement, x')
xlim([0,2])
ylabel('\color{black}\fontsize{12}\bf Concentration, c')
hold off

figure(3)
plot (x,z,'b')                   % plot initial
hold on
plot (x,freal,'gx')               % plot real 
hold on
plot (x,flw,'k')                 % plot Lax-Wendroff
hold off

title('\color{black}\fontsize{12}\bf Concentration Profile of Plume')
legend('Initial','Real','Lax-Wendroff')
set (gca, 'fontsize', 14)
xlabel('\color{black}\fontsize{12}\bf Displacement, x')
xlim([0,2])
ylabel('\color{black}\fontsize{12}\bf Concentration, c')
...