Heat Conduction in 1D with Finite Differences

Hello. I want to plto/simulate the temperature distribution of the following equation and statements:

Here is my code:

clear
clc
clf

L =1; %length

alpha = 1;
xmin = 0;
xmax = L;

N = 100; %number of nodes

dx = (xmax-xmin)/(N-1);
x = xmin:dx:xmax;

x0 = 0:dx/2:L/2;        %values of x for the firs line T0=2x
xL = L/2:dx/2:L;        %values of x for the second line TL=2(1-x)

dt = 4.000E-5;
tmax = 1;
t = 0:dt:tmax;

% problem initialization
T0 = ones(1,N).*(2*x0);
TL = ones(1,N).*(2-2*xL);

% solving the problem
r = alpha*dt/(dx^2); % for stability, must be 0.5 or less

for j = 2:length(t) % for time steps
    T = [T0 TL];  
 
    for i = 1:N % for space steps
        if i == 1 || i == N
            T(i) = 0;
        else
            T0(i) = T0(i)+r*(T0(i+1)-2*T0(i)+T0(i-1)); %values of temperature for 0 < x < L/2
            TL(i) = TL(i)+r*(TL(i+1)-2*TL(i)+TL(i-1)); %values of temperature for L/2 < x < L
        end
    end
    T = [T0 TL];
    plot(x,T)
    shg
    pause(0.005)
end

Im having difficulty troubleshooting the code. I can't quite get x and T to be the same size in order to plot. I was hoping someone might shed some light on what be wrong. Thank you!

Answer 1

[darova]

I have some suggestions to your code. Look

[sabrina sierra]

It worked wonderfully! I forgot to add it to the question but, can you help with using a mesh to plot the temperature through time and space? Can it be done in this case?

[darova]

Sure, here is an example

T = [T0 TL];                    % X direction (columns)
T = repmat(T,[100 1]);          % make 100 points in time direction (rows)
h = surf(T);                    % display
for i = 1:size(T,1)-1
    for j = 2:size(T,2)-1
        T(i+1,j) = T(i,j) + r*(T(i,j+1)-2*T(i,j)+T(i,j-1));
    end
    set(h,'zdata',T)
    pause(0.01)
end

[darova]

Pay attention that im not plotting inside for loop. Only changing z data inside. It's much faster