How to perform iteration calculations

If we are given a set of data and we know that (Tx-T9)/(T1-T9) = cosh[m(L-x)]/cosh(mL), where the only unknown is m, how could we do the iteration calculations on Matlab?

Can we simply solve for m or is the iteration process necessary? We are assuming that m is initially equal to 7.4 m^-1. I tried using Excel for iteration calculations, but I couldn't obtain the value for m for the last 3 temperatures.

Thank you for your help!

Answer 1

[Matt J]

You can use fzero,

     fun=@(m) norm((Tx-T9)./(T1-T9) - cosh(m(L-x))./cosh(mL));

     m = fzero(fun,m0);

Here m0=7.4 is your initial guess. You could also plot the function and look for an approximate root graphically.

[dj]

Ok, this is what I'm doing:

L = 0.35; T9 = 27.4; T1 = 49.7; Tx = 42.5; x = 0.05; m0 = 7.4;

fun=@(m)norm((Tx-T9)./(T1-T9) - cosh(m*(L-x))./cosh(m*L));

m = fzero(fun,m0);

It tells me that "Exiting fzero: aborting search for an interval containing a sign change because NaN or Inf function value encountered during search. (Function value at -2417.43 is NaN.) Check function or try again with a different starting value."

Could you tell me why it's not giving me a value close to 7.4? In Excel, I got a value close to 7.2.

[Matt J]

Sorry, I thought x was a vector of data, in which case you would use fminsearch instead of fzero. But since all data are scalars, you can do as follows,

      L = 0.35; T9 = 27.4; T1 = 49.7; Tx = 42.5; x = 0.05; m0 = 7.4;

      A=(Tx-T9)./(T1-T9); %pre-compute to conserve computation
      B=L-x;

      fun=@(m) A- cosh(m*B)./cosh(m*L);

      [m,fval] = fzero(fun,m0)

from which I get the result

    m =

        7.8930

    fval =

         0

[dj]

x was a vector of data (x1, ...xn), but I just decided to type in values one by one 'cause I didn't know how to calculate all of the values at the same time, haha. I was wondering why I couldn't get a nice enough answer, but I realized that I was using the wrong values for T9. Thank you so much!