code is right but can not the a plot

Hello, I do not what the mistake is? I'm getting the first plot. However, I have not been able to get the second plot. Not sure how to fix it. As alwyas any help will be greatly appreciated. Thanks

clear
clc

L = 1-0;
T = 0.06-0;
alpha = 1;
dx = 0.05;
dt = 0.001;
%Q = (alpha.*dt)/(dx.^2);
Q = 0.25;
N = L/dx +1;
M = T/dt + 1;  
x = zeros(N,1);
t = zeros(M,1);


for i=1:N
    x(i) = 0+(i-1).*dx;
end

for n=1:M
    t(n) = 0+(n-1).*dt;
end
u = zeros(M,N);
u(:,1) = 2;
u(:,N) = 1;
u(1,2:N-1) = sin(pi.*x(2:N-1));

for n=1:M
  for i=2:N-1
    u(n+1,i) = Q.*u(n,i+1) + (1-2*Q).*u(n,i) + Q.*u(n,i-1)  
  end
end
figure(1)
plot (x,u(M,:)) %plot x vs u
title ('x vs u at t = 0.06')
xlabel ('x')
ylabel ('T')
grid on

figure(2)
plot(t, u(:,N-1)) %plot t vs u
title ('t vs u at x = 0.5')
xlabel ('time')
ylabel ('T')

[Cesar Cardenas]

thank you. could you show me the lines where the problem is? I did not write the whole code, I just added a couple of lines to plot. Thank you.

Answer 1

[Star Strider]

You need to redefine ‘t’ so that it matches the row size of ‘u’:

t = linspace(0, 2.5, size(u,1));

Try this —

% clear
% clc

L = 1-0;
T = 0.06-0;
alpha = 1;
dx = 0.05;
dt = 0.001;
%Q = (alpha.*dt)/(dx.^2);
Q = 0.25;
N = L/dx +1;
M = T/dt + 1;  
%x = zeros(N,1);
x = linspace(0, 2.5, 5);
% t = linspace(0, 2.5, 5);
%t = zeros(M,1);


for i=1:N
    x(i) = 0+(i-1).*dx;
end

for n=1:M
    t(n) = 0+(n-1).*dt;
end
u = zeros(M,N);
u(:,1) = 2;
u(:,N) = 1;
u(1,2:N-1) = sin(pi.*x(2:N-1));

for n=1:M
  for i=2:N-1
    u(n+1,i) = Q.*u(n,i+1) + (1-2*Q).*u(n,i) + Q.*u(n,i-1);  
  end
end

figure(1)
plot (x,u(M,:)) %plot x vs u
title ('x vs u at t = 0.06')
xlabel ('x')
ylabel ('T')
grid on

t = linspace(0, 2.5, size(u,1));                                        % Redefine 't' To Match 'u'

figure(2)
plot(t, u(:,N-1)) %plot t vs u
title ('t vs u at x = 0.5')
xlabel ('time')
ylabel ('T')

EDIT — Forgot to re-run code before posting. Now run.

.

[Torsten]

@Star Strider

By changing t before plotting, u(:,N-1) is plotted at the wrong times.

Answer 2

[Torsten]

If you compare size(t) and size(u,1), you will find that the number of elements of both vectors are not the same (they differ by one element). Thus the second plot command errors.

Replace

for n=1:M
    for i=2:N-1
        u(n+1,i) = Q.*u(n,i+1) + (1-2*Q).*u(n,i) + Q.*u(n,i-1)  
    end
end

by

for n=1:M-1
    for i=2:N-1
        u(n+1,i) = Q.*u(n,i+1) + (1-2*Q).*u(n,i) + Q.*u(n,i-1)  
    end
end