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)");

[Shaun Hamilton]

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.

[jlvdoorn]

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.

Answer 1

[Sulaymon Eshkabilov]

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.

[jlvdoorn]

Thnx!

@Sulaymon Eshkabilov it is working now!

[Sulaymon Eshkabilov]

You're welcome! It is a pleasure.

[jlvdoorn]

Thnx, Now I am having a new (somewhat same) problem.

I need to plot this function at t = 0.1 and x = 0.5, y=0:0.1:1. alpha = 1e-4.

Could you please help me again?

Many thnx!!

[Sulaymon Eshkabilov]

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.

[jlvdoorn]

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

[Sulaymon Eshkabilov]

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.