MATLAB Answers

0

Plotting Sum of series

Hi all,
I want to plot the tempersature distribution:
For x = 0.5 (constant) and y =0:0.1:2;
I used the code below which give me an error:
Error using plot
Data must be numeric, datetime, duration or an array convertible to double.
What am I doing wrong?
Thnx
Jan
clear
clc
x = 0.5;
h = 0.1;
ymax = 2;
y = 0:h:ymax;
syms n
T = 273+symsum(400/sinh(2*pi*n)*n*pi*(1-((-1)^n)*cos(1))/((1-(n^2)*(pi^2))^2)*sin(n*pi*x)*sinh(n*pi*y), n, 1, Inf);
plot(T,y);
xlegend("Static Temperature (c)");
ylegend("Position (m)");

  2 Comments

If you look at the output of T, you can see why you are not getting a plot. I would, plot each of the four answers for T.
symsum is defined as
symsum(function, variable, lower boundry, upper boundry)
It is a summation from n=1 to n=Inf over the function mentioned above.

Sign in to comment.

Products


Release

R2019b

1 Answer

Answer by Sulaymon Eshkabilov on 12 Oct 2019
 Accepted Answer

Hi,
In your exercise, it is more appropriate to use numerical solution approach instead of symbolic math. Here is one of the possibe solutions:
x = 0.5;
h = 0.1;
ymax = 2;
y = 0:h:ymax; T(1,:)=273*ones(size(y));
for n=1:5-1
for m = 1:numel(y)
T(n+1,m) = T(n,m)+sum(400/sinh(2*pi*n)*n*pi*(1-((-1)^n)*cos(1))/((1-(n^2)*(pi^2))^2)*sin(n*pi*x)*sinh(n*pi*y(m)));
end
end
%%
plot(y, T);
xlabel("Static Temperature (c)");
ylabel("Position (m)");
Good luck.

  6 Comments

Hi,
This exercise is pretty much the same as the previous on, e.g.:
x = 0.5;
h = 0.1;
ymax = 2;
y = 0:h:ymax; T(1,:)=ones(size(y));
for n=1:5-1
for m = 1:numel(y)
T(n+1,m) = T(n,m)+(48/(pi^6))*sum(((-1^n)/(n^3))*((-1^m)-1)/(m^3))*...;
end
end
Good luck.
Thanks for your answer, unfortunately it is not working :(
It gives me a 5 x 21 matrix for T. But I expected an array of length: numel(y).
Could you please help me one last time?
clear
clc
a = 1e-4;
t = 0.1;
x = 0.5;
h = 0.1;
ymax = 2;
y = 0:h:ymax;
T(1,:)=ones(size(y));
for n=1:5-1
for m = 1:numel(y)
T(n+1,m) = T(n,m)+(48/(pi^6))*sum(((-1^n)/(n^3))*((-1^m)-1)/(m^3))*sin(n*pi*x)*sin(m*pi*y(m))*exp(-(n^2+m^2)*pi^2*a*t);
end
end
Hi
From your question, I see that you'd like to set n = 1. If so, the loop will be:
T(1,:)=ones(size(y)); n=1;
for m = 1:numel(y)
T(1,m) = T(n,m)+(48/(pi^6))*sum(((-1^n)/(n^3))*((-1^m)-1)/(m^3))*sin(n*pi*x)*sin(m*pi*y(m))*exp(-(n^2+m^2)*pi^2*a*t);
end
Good luck.

Sign in to comment.