using fzero to solve nonlinear equation

I have the nonlinear equation

I need to use fzero to solve for s at different times, t.

In my script, I defined known parameters, created a function handle for the nonlinear equation set to zero, created a loop to calculate concentration at each time point, and within the loop used the fzero function. For my estimation I used 8, as a graph created earlier in the problem seems to approach 0 around 10. As shown in the command window there seems to be missing inputs within my function. However, I have checked thoroughly for missing inputs and even utilized the function outside of fzero and it worked fine. I assume the issue is then with fzero, but I am not sure what it is. Any advice is welcome!

Answer 1

[Walter Roberson]

The function handle you pass to fzero() or to fsolve() must accept only one parameter.

Your s0, vmax, and k are all known constants, and do not need to be passed to the function; when you create the anonymous function, MATLAB will pull them out of the current workspace.

Your code suggests that you are trying to find s that satisfies the expression, but your text description indicates you need to find t ?

[Jordan Rosales]

When I set (t) as the only function handle input, it returns the error:

Operands to the || and && operators must be convertible to logical scalar values.

Error in fzero (line 307)

elseif ~isfinite(fx) || ~isreal(fx)

Error in rosalesLab101 (line 31)

s(i)=fzero(conc,8);

I am not quite sure what this means

[Walter Roberson]

No loop needed:

s = arrayfun(@(T) fzero(@(s) km*log(s0/s) + (s0-s) - vmax*T, 8), t)

[Jordan Rosales]

what is 'T' in this solution?

[Walter Roberson]

T is a dummy variable in an anonymous function. arrayfun() in that form will take each value of t and substitute one value at a time for T into fzero(@(s) km*log(s0/s) + (s0-s) - vmax*T, 8) and collect all of the results.

If you prefer to loop then

tvals = 0:0.1:10;
numt = numel(tvals);
s = zeros(size(tvals));
for tidx = 1 : numt
   t = tvals(tidx);
   s(tidx) = fzero(@(S) km*log(s0/S) + (s0-S) - vmax*t, 8);
end