How to get sinusodial behaviour from 2nd order ode using function handle?

function[dtheta] = FiniteConduct(x,t,alph,L)
n=[1:10]

dtfh= @(t) 1-x./L -2 ./pi.*sum(1 ./n .*exp(-alph.*t.*((n.*pi/L).^2)).*sin(n.*pi.*x./L));
dtheta = dtfh(t(1));

  for (k=1:numel(t)-1)
    for (n = 1:10)
      for (x = [0:.01:.1])
        x = x+1;
        if(x<L)
        n=n+1;
        dtheta(k+1) = dtheta(k) + dtfh(t(k+1))
         else
          x = L;
         end
      end
   
    end
end
end

There seems to be something wrong with my function handle and the way I have implemented the sigma notation for sum? im trying to use convert this equation below into a function handle.

Answer 1

[Alan Stevens]

You coud try implementing the function along these lines (obviously, you will need to use your own values for alpha etc):

alpha = 0.1;
L = 1;
t = 0.1;
x = 0:0.01:1;
for i = 1:numel(x)
    theta(i) = dtfh(x(i),t,alpha,L);
end
plot(x,theta)

function theta = dtfh(x,t,alpha,L)
      
         S = 0;
         Sold = 100;
         n = 0;
         while abs(S-Sold)>1e-8
             
             Sold = S;
             n = n+1;
             S = 1/n*exp(-alpha*t*(n*pi/L)^2)*sin(n*pi*x/L) + S;
             
         end
         theta = 1 - x/L - 2/pi*S;
         
end

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