Equation code and plots

Hello, just wanted to know if this code would be fine for this equation? and how I could get some plots and get some error results? 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) = 0;
u(:,N) = 0;
u(M,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

Answer 1

[Dyuman Joshi]

I did some tweaks here and there, rest of the code is good.

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;  

%Vectorize the definition of x and t
x = (0:N-1)*dx;
t = (0:M-1)*dt;


u = zeros(M,N);
%These two lines are redundant
%u(:,1) = 0;
%u(:,N) = 0;
u(M,2:N-1) = sin(pi.*x(2:N-1));

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

What do you want to plot? And do you have any data to find error against?

[Cesar Cardenas]

Thank you, I would like to plot u, but not sure how to do ti? no, I do not have any data.

[Cesar Cardenas]

This is what I'm trying to plot, but I'm getting errors.

Error using plot

Vectors must be the same length.

Error in HW1 (line 31)

plot(t, u(:,(N-1)/2)) %plot t vs u

As always any help wil be appreciated.

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;  
%Vectorize the definition of x and t
x = (0:N-1)*dx;
t = (0:M-1)*dt;
u = zeros(M,N);
%These two lines are redundant
%u(:,1) = 0;
%u(:,N) = 0;
u(M,2:N-1) = sin(pi.*x(2:N-1));
for n=1:M
    for m=2:N-1
        u(n+1,m) = Q.*u(n,m+1) + (1-2*Q).*u(n,m) + Q.*u(n,m-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')

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

[Dyuman Joshi]

plot U with respect to what? Generally, you need x and y values for a plot.

If you don't have any data, how do you want to calculate the error?

[Cesar Cardenas]

ok can you tell me what I'm missing to get the plots?

[Dyuman Joshi]

Are use sure about this line?

u(M,2:N-1) = sin(pi.*x(2:N-1));

I think that it should be 1 instead of M, otherwise all the values in u are zero (check below)

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;
%Vectorize the definition of x and t
x = (0:N-1)*dx;
t = (0:M-1)*dt;

u = zeros(M,N);
u(M,2:N-1) = sin(pi.*x(2:N-1));

In the outer for loop below, if n is 1:M, then n+1 is 2:M+1, which creates an extra row in u, causing the error below in the plot. I modified it to 1:M-1.

for n=1:M-1
    for m=2:N-1
        u(n+1,m) = Q.*u(n,m+1) + (1-2*Q).*u(n,m) + Q.*u(n,m-1);
    end
end
%Verifying that all the values in u are zero
all(u==0,'all')

ans = logical
   1

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

figure(2)
plot(t', u(:,(N-1)/2)) %plot t vs u
%You need to take transpose of any one input
%as t is a row vector and u(:,(N-1)/2) is a column vector
title ('t vs u at x = 0.5')
xlabel ('time')
ylabel ('T')