error when i want to run it

function linearAdvection_JA
clear  % Clears workspace
clc   % Clears history
clf   % Clears figure window
N = 101;  % Defines the no. of grid points
p = 0;   % Sets the lower end of the domain
q = 100; % Sets the upper end of the domain
v = 0.8;  % defines velocity of the water (meters)
dx = (q - p)/(N - 1); % Calculates the grid spacing
dt = 0.8; % Defines the time step.
t = 0;  % Sets the initial time to zero
runtime = 100;  % Defines time program runs for
s = 0.4;    % Sets safety factor to 0.4 (Advised not to change this)
pausetime = 0.1;   % Pause time between animation
L=1;
x = p : dx : q; % Calculates the value of x using the domain and the grid spacing
for i = 1 : N
    U(i) = exp(-(x(i)-L/2).^2);  % Defines the initial pollutant using initial conditions
end
% fprintf('Select a scheme from the list and enter the corrosponding number \n\nFirst Order Upwind - 1\nLax-Friedrichs - 2 \nLax-Wendroff - 3\nAdams Average (Lax-Friedrichs) - 4\nAdams Average (Lax-Wendroff) - 5\n\n')   
Choice = input('Scheme no. = ');   % Select a scheme to run
if Choice == 2 
     A = 1;
    B = 1;          % <<<< DO NOT CHANGE THESE VALUES 
    C = 0;
elseif Choice == 3   
    A = 1;
    B = 1;          % <<<< DO NOT CHANGE THESE VALUES 
    C = 0;
elseif Choice == 4 
    A = 2;
    B = 2;         % <<<<< Values can be changed
    C = 1;
elseif Choice == 5 
    A = 1;
    B = 1;        % <<<<<<<< Values can be changed 
    C = 5;
end
% ===================== Runs similation ===================================
while t < runtime  % Halts program when inequality is violated
    % Applies periodic boundary conditions depending on choice
    if Choice == 1
        boundary1 = un(N);
        boundary2 = un(1);
        un = [boundary1 un(1:N-1) boundary2];
    elseif Choice == 2 
        boundary1 = un(N);
        boundary2 = un(1);
        un = [boundary1 un boundary2];
        elseif Choice == 3 
        boundary1 = un(N);
        boundary2 = un(1);
        un = [boundary1 un boundary2];
        elseif Choice == 4 
        boundary1 = un(N);
        boundary2 = un(1);
        un = [boundary1 un boundary2]; 
         elseif Choice == 5 
        boundary1 = un(N);
        boundary2 = un(1);
        un = [boundary1 un boundary2];
    end
    
    dt = s * dx / v;  % Calculates time step 
    t = t + dt;   % Adds time step to time 
    
    c = dt/dx;  % Calculates this here to provide efficiency
    
    if Choice == 1  % Applies First Order Upwind scheme
        for j = 2 : N + 1
            u(j) = un(j) - v * c * (un(j) - un(j-1)); 
        end
    elseif Choice == 2  % Applies either Lax-Friedrichs or Adams Average (Lax-Friedrichs) scheme
        for j = 2 : N + 1
            u(j) = (A*un(j+1) + B*un(j-1) + C*un(j))/(A+B+C) - v * c * (un(j+1) - un(j-1)); 
        end
        elseif Choice == 4  % Applies either Lax-Friedrichs or Adams Average (Lax-Friedrichs) scheme
        for j = 2 : N + 1
            u(j) = (A*un(j+1) + B*un(j-1) + C*un(j))/(A+B+C) - v * c * (un(j+1) - un(j-1)); 
        end
    elseif Choice == 3   % Applies either Lax-Wendroff or Adams Average (Lax-Wendroff) scheme
        for j = 2 : N + 1
            u(j) = (A*un(j+1) + B*un(j-1) + C*un(j))/(A+B+C) - v * c * (un(j+1) - un(j-1))/2 + c^2 * v^2 * 0.5 * (un(j+1) - 2*un(j) + un(j-1)); 
        end
         elseif Choice == 5   % Applies either Lax-Wendroff or Adams Average (Lax-Wendroff) scheme
        for j = 2 : N + 1
            u(j) = (A*un(j+1) + B*un(j-1) + C*un(j))/(A+B+C) - v * c * (un(j+1) - un(j-1))/2 + c^2 * v^2 * 0.5 * (un(j+1) - 2*un(j) + un(j-1)); 
        end
    end
    
    plot(x,u(2:N+1),'b')    % Plots pollutant (dependent variable)
    xlabel('x [m]')         % Adds appropiate labels
    ylabel('U [m]')
    
    % Adds title depending on scheme choice
    
    if Choice == 1
        title('Solves 1D Advection Equation using FOU Scheme','Fontsize',10)
    elseif Choice == 2
        title('Solves 1D Advection Equation using Lax-Friedrichs Scheme','Fontsize',10)
    elseif Choice == 3
        title('Solves 1D Advection Equation using Lax-Wendroff Scheme','Fontsize',10)
    elseif Choice == 4
        title('Solves 1D Advection Equation using Adams Average (Lax-Friedrichs) Scheme','Fontsize',10)
    elseif Choice == 5
        title('Solves 1D Advection Equation using Adams Average (Lax-Wendroff) Scheme','Fontsize',10)
    end
    
    axis([p q min(u) 1.1*max(u)])  % Sets axis 
    pause(pausetime)   % Shows results for each timestep
    
    un = u(2:N+1);   % Ommits boundary conditions ready for the next time step
  
end
end
function initial = U(x) % Defines initial conditions.
pollutantstart1 = 20;   % Start of pollutant concentration 1
pollutantend1 = 40;     % End of pollutant concentration 1
pollutantstart2 = 60;   % Start of pollutant concentration 2
pollutantend2 = 80;     % End of pollutant concentration 2
pollutantfloor = 0.1;  % Defines bottom of pollutant
pollutantpeak = 0.8;   % Defines top of pollutant
initial = pollutantfloor;   % Sets up bottom of pollutant 
% ============ Determins the areas in which the pollutant peaks ==========
if x >= pollutantstart1 && x <= pollutantend1
    initial = pollutantpeak;
elseif x >= pollutantstart2 && x <= pollutantend2
    initial = pollutantpeak;
end
end

[Walter Roberson]

What error are you encountering?

[lulu]

it is coming the following erro

Reference to a cleared variable u.

Error in linearAdvection_JA (line 91)

plot(x,u(2:N+1),'b') % Plots pollutant (dependent variable)

[lulu]

and no graph coming

i just write the equation on initial condition

Answer 1

[Walter Roberson]

You should not typically use clear in a function, except sometimes to clear a large variable that takes up a significant fraction of memory.

Your code should be written to check the value of Choice when you get it from the user, to verify that it is 1, 2, 3, 4, or 5. You might want to consider using menu() instead of input() there.

Your current code does not create u unless Choice is one of those 5 numbers.