Matlab code for the Formula
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Following is the Analytical solution of a Heat Diffusion formula where x is length of Rod from 0 to 1 meter with an increment of 0.1. Also t is the time from 0 to 10 minute with an increment of 1 min. Value of r is 0.1. The result should almost match with the following table
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/171424/image.jpeg)
. The result in the table was obtained using the Numerical Method (Explicit Method) of the problem.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/171425/image.jpeg)
I've tried the following code:
close all clear clc
x = 0:0.1:1; t = 0:1:10; r = 0.1; [X,T] = meshgrid(x,t) S = 0;
for n=1:1e6 S = S + sin(pi*n/2)*sin(n*pi*X).*exp(-n*n*r*r*t)/(n*n); end U = (8/pi*pi)*S
What is wrong with this code?
2 Comments
John D'Errico
on 21 Mar 2018
Edited: John D'Errico
on 21 Mar 2018
What have you tried? If nothing, why not? It is by making an effort that you will learn, not by being given the solution to your homework on a platter. So show what you tried. If you do, you will have abetter chance of getting some help here.
Answers (2)
Image Analyst
on 21 Mar 2018
One way is a more direct, though not vectorized, approach of using for loops over t and x:
x = 0:0.1:1;
t = 0:1:10;
r = 0.1;
U = zeros(length(t), length(x));
for kt = 1 : length(t)
for kx = 1 : length(x)
s = 0;
for n=1:1e6
s = s + sin(pi*n/2).*sin(n*pi*x(kx)).*exp(-n*n*r*r*t(kt))/(n*n);
end
U(kt, kx) = 8 * s / pi^2;
end
end
U
0 Comments
Abraham Boayue
on 21 Mar 2018
Edited: Abraham Boayue
on 21 Mar 2018
Hey Rasel, your code was almost right. You made just a few errors, instead of initializing the sum as you did, you should have just initialized U as a matrix. This is your code with a few changes.
clear variables
close all
x = 0:0.1:1;
t = 0:10;
r = 0.1;
N = length(x);
M = length(t);
U = zeros(N,M); % This is what you should have done to start with.
[x,t] = meshgrid(x,t);
for n = 1: 100
U = U + ((1/n^2)*sin(0.5*pi*n)*sin(pi*n*x).*exp(-n^2*r^2*t))';
end
U = (8/pi.^2)*U;
disp(U')
figure
surf(x,t,U')
grid
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