Surf Question/ Data dimensions must agree

I am trying to create a dufort frankel scheme. This is a textbook code. I am having trouble repeatedly with line 71 error using surf, data dimensions must agree, then error in line 74 surf(x, tt, u'). I am unsure of what this means. Could someone please inform me of the error and how to correct in detail?

clear all;                  % clear all variables in memory
 
xl=0; xr=1;                 % x domain [xl,xr]
J = 10;                     % J: number of division for x
dx = (xr-xl) / J;           % dx: mesh size
tf = 0.1;                   % final simulation time
Nt = 50;                    % Nt: number of time steps
dt = tf/Nt; 
k = 0;
t = 0;
 
mu = dt/(dx)^2; 
 
if mu > 0.5         % make sure dt satisy stability condition
    error('mu should < 0.5!')
end
% Evaluate the initial conditions
x = xl : dx : xr;              % generate the grid point
% f(1:J+1) since array index starts from 1
f = sin(pi*x) + sin(2*pi*x);  
 
% store the solution at all grid points for all time steps
u = zeros(J+1,Nt+1);   
 
% Find the approximate solution at each time step
for n = 1:Nt
    t = n*dt;         % current time
   
    % boundary condition at left side
    gl = sin(pi*xl)*exp(-pi*pi*t)+sin(2*pi*xl)*exp(-4*pi*pi*t);   
    % boundary condition at right side
    gr = sin(pi*xr)*exp(-pi*pi*t)+sin(2*pi*xr)*exp(-4*pi*pi*t);  
    if n==1    % first time step
       for j=2:J    % interior nodes     
       u(j,n) = f(j) + mu*2*(f(j+1)-(f(j)+f(j))+f(j-1));
       end     
       u(1,n) = gl;   % the left-end point
       u(J+1,n) = gr; % the right-end point 
    else 
       for j=2:J    % interior nodes
         u(j+1,n)=u(j,n-1)+mu*2*(u(j,n+1)-(u(j-1,n)+u(j+1,n))+u(j,n-1));
       end
       u(1,n) = gl;   % the left-end point
       u(J+1,n) = gr; % the right-end point 
    end
    
    % calculate the analytic solution 
   
    for j=1:J+1
        xj = xl + (j-1)*dx;
        u_ex(j,n)=sin(pi*xj)*exp(-pi*pi*t) ...
+sin(2*pi*xj)*exp(-4*pi*pi*t);
    end
end
 
% Plot the results
tt = dt : dt : Nt*dt;
figure(1)
colormap(gray);     % draw gray figure
surf(x,tt, u');     % 3-D surface plot
xlabel('x')
ylabel('t')
zlabel('u')
title('Numerical solution of 1-D parabolic equation')
 
figure(2)
surf(x,tt, u_ex');     % 3-D surface plot
xlabel('x')
ylabel('t')
zlabel('u')
title('Analytic solution of 1-D parabolic equation')
 
maxerr=max(max(abs(u-u_ex)));

[per isakson]

You might want to try to fix your code with the help of: Debug a MATLAB Program and Examine Values While Debugging

Answer 1

[KSSV]

YOu have asked this question already here: https://in.mathworks.com/matlabcentral/answers/449546-problem-with-index-dufort-frankel-scheme?s_tid=prof_contriblnk . I have corrected your code..you have not acknowledged it and you didn't discuss it. You should close your question by accepting the answer if it worked for you and then ask the second next question.

xl=0; xr=1;                 % x domain [xl,xr]
J = 10;                     % J: number of division for x
dx = (xr-xl) / J;           % dx: mesh size
tf = 0.1;                   % final simulation time
Nt = 50;                    % Nt: number of time steps
dt = tf/Nt;
k = 0;
t = 0;

mu = dt/(dx)^2;

if mu > 0.5         % make sure dt satisy stability condition
    error('mu should < 0.5!')
end
% Evaluate the initial conditions
x = xl : dx : xr;              % generate the grid point
% f(1:J+1) since array index starts from 1
f = sin(pi*x) + sin(2*pi*x);

% store the solution at all grid points for all time steps
u = zeros(J+1,Nt+1);
u_ex = u ;
% Find the approximate solution at each time step
for n = 1:Nt
    t = n*dt;         % current time
    
    % boundary condition at left side
    gl = sin(pi*xl)*exp(-pi*pi*t)+sin(2*pi*xl)*exp(-4*pi*pi*t);
    % boundary condition at right side
    gr = sin(pi*xr)*exp(-pi*pi*t)+sin(2*pi*xr)*exp(-4*pi*pi*t);
    if n==1    % first time step
        for j=2:J    % interior nodes
            u(j,n) = f(j) + mu*2*(f(j+1)-(f(j)+f(j))+f(j-1));
        end
        u(1,n) = gl;   % the left-end point
        u(J+1,n) = gr; % the right-end point
    else
        for j=2:J    % interior nodes
            u(j+1,n)=u(j,n-1)+mu*2*(u(j,n+1)-(u(j-1,n)+u(j+1,n))+u(j,n-1));
        end
        u(1,n) = gl;   % the left-end point
        u(J+1,n) = gr; % the right-end point
    end
    
    % calculate the analytic solution
    
    for j=1:J+1
        xj = xl + (j-1)*dx;
        u_ex(j,n)=sin(pi*xj)*exp(-pi*pi*t) ...
            +sin(2*pi*xj)*exp(-4*pi*pi*t);
    end
end

% Plot the results
tt = dt : dt : (Nt+1)*dt;
figure(1)
colormap(gray);     % draw gray figure
surf(x,tt, u');     % 3-D surface plot
xlabel('x')
ylabel('t')
zlabel('u')
title('Numerical solution of 1-D parabolic equation')

figure(2)
surf(x,tt, u_ex');     % 3-D surface plot
xlabel('x')
ylabel('t')
zlabel('u')
title('Analytic solution of 1-D parabolic equation')

maxerr=max(max(abs(u-u_ex)));