Surface Plot in Sum Series

Hello, I've successfully express the Sum Series, but I have a small issue on implementing it surface plot.

I attempt I'm various methods, but always have the error: "Error using surf (line 71): Z must be a matrix, not a scalar or vector."

I would appreciate if anyone can figure out any small modifications on the surf plot.

h=2;
v=2;
l=2;

a = linspace(-5,5,100);
b = linspace(-5,5,100);
[x t]=meshgrid(a,b);

syms x t m

f = (8*h/pi^2)*(((-1)^(m-1))/((2*m-1)^2))*sin(((2*m-1)*pi*v*x)/l)*cos(((2*m-1)*pi*v*t)/l);
sum_f = symsum(f,m,1,Inf);


surf(x,t,sum_f);

Answer 1

[KSSV]

h=2;
v=2;
l=2;

a = linspace(-5,5,100);
b = linspace(-5,5,100);
[x, t]=meshgrid(a,b);


m = 1000 ; 
for i = 1:m
    f = (8*h/pi^2)*(((-1)^(m-1))/((2*m-1)^2))*sin(((2*m-1)*pi*v*x)/l).*cos(((2*m-1)*pi*v*t)/l);
end
% sum_f = symsum(f,m,1,Inf);


surf(x,t,f);

[Charles Thomas]

Thank You very much! I really appreciate your help.

[KSSV]

Thanks is accepting and/or voting the answer. :)

[Grant Recker]

I think you want to make a few changes to the code if I understand the question correctly.

The loop in the example code repeats the same calculation over and over and doesn't generate the sum. To fix that we can switch m and i. We can also record the results of f for each iteration of m.

Here i is the number of iterations and m is the summation index, and f is now the sum of the result of the equation.

h=2;
v=2;
l=2;

r=100; % resolution of the grid

a = linspace(-5,5,r);
b = linspace(-5,5,r);
[x, t]=meshgrid(a,b);

f=zeros(r);

i = 1000 ; % number of iterations
for m = 1:i
    f = f + (8*h/pi^2)*(((-1)^(m-1))/((2*m-1)^2))*sin(((2*m-1)*pi*v*x)/l).*cos(((2*m-1)*pi*v*t)/l);
end

surf(x,t,f);