Why does fsolve not return the correct solution?

Question

Radu Bors 2020-3-21

0
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https://ww2.mathworks.cn/matlabcentral/answers/512120-why-does-fsolve-not-return-the-correct-solution

评论： Radu Bors 2020-3-23

采纳的回答： darova

在 MATLAB Online 中打开

I have an implicit function:

which I am trying to solve using fsolve to get the roots of the function f(j) below.

I know what my solutions should be from some experimental data. But when I run the code below to get the solution of the implicit function, it doesn't look at all correct.

E_data = sortrows(data(:,3))';
j_exp_data = sortrows(data(:,2))';
E = 0;
f = @(j)...
j_a * exp(  (alpha_anod * z * Faraday_const) / (R_const * T) * (E  - j*R - E_eq)) - ...
j_c * exp( -(alpha_cath * z * Faraday_const) / (R_const * T) * (E  - j*R - E_eq)) - j;
for i = 1:length(E_data)
    E = E_data(i);
    [j_sol(i), fval(i), flag(i)] = fsolve(f, j_exp_data(i));
end
%% 
figure
subplot(1,2,1)
plot(E_data, j_sol);
title("Implicit function solution");
grid on;
subplot(1,2,2)
plot(E_data, j_exp_data);
title("Experimental data");
grid on;

I'm getting some weird solution (see below). As a starting value for fsolve, I'm using the experimental value. I don't expect them to be exactly the same, but it should be close enough. Instead, I get completely off values: