# Use fsolve with an elliptic integral

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carlos Hernando on 17 Mar 2020
Commented: carlos Hernando on 17 Mar 2020
Hello,
I need to solve a non-linear equation with an eliptic integral in it. I tried to used fsolve but it don't want to work, any ideas. I copy the code below:
NI = 6.749914199660242e+05;
NI_ol = 1.749914199660242e+05;
Muo = 4*pi*10^-7; % (T*m/A)
a = 0.2073;
y = 0.15;
% Bos_c = Muo*(NI-NI_ol)*(a^2)/((z(1)^2 + a^2)^(1.5));
% m = (4*a*y)/((a+y)^2+z(1)^2);
%
% [K, E]= ellipke(m);
% Be = 2*Muo*NI*a*((2*m)^0.5)*(a*m*E/(2-2*m) + y*K - y*(2-m)*E/(2-2*m))/(2*pi*(2*a*y)^(1.5));
F=@(z) [Muo*(NI-NI_ol)*(a^2)/((z(1)^2 + a^2)^(1.5))...
- 2*Muo*NI*a*((2*m)^0.5)*(a*m*E/(2-2*m) + y*K - y*(2-m)*E/(2-2*m))/(2*pi*(2*a*y)^(1.5));...
m - (4*a*y)/((a+y)^2+z(1)^2);
[K, E]== ellipke(m)];
z_c = [0; 1000];
opts = optimoptions(@fsolve,'Algorithm', 'levenberg-marquardt');
neff = fsolve(F,z_c,opts);

Matt J on 17 Mar 2020
Edited: Matt J on 17 Mar 2020
It does not make sense to have a relational expression like,
[K, E]== ellipke(m)
as one of your equations, expecially one that doesn't depend on any of your unknowns, z(i). Also, z(2) is not used anywhere in the system of equations. In other words, you have multiple equations in a single unknown z(1), so the system is not likely to have a solution.
carlos Hernando on 17 Mar 2020
Ok I sort it out, just eliminating opts seems to work.
Thank you Matt