fsolve stopped because it exceeded the function evaluation limit, options.Ma​xFunctionE​valuations = 400 (the default value).

So I am trying to solve system of equations using fsolve but the message above keeps showing, here is my code

clc; clear; close all;
global X L2 t2 t1 h
L2= 4.42;
X= 4; t2= 100*pi/180; t1=50*pi/180; h=0.5; %initial values%
x= fsolve(@SiccorLift,[X;t2;t1;h]);
X= x(1); t2= x(2)*180/pi; t1= x(3)*180/pi; h= x(4);
function F= SiccorLift(x)
global L2
F(1) = x(1) + L2*cos(x(2)) - 5*cos(x(3));
F(2) = L2*sin(x(2))- 5*sin(x(3));
F(3)= x(1)+ 8*cos(x(3));
F(4)= 8*sin(x(3)) - x(4);
end

Answer 1

[Walter Roberson]

Use options.

https://www.mathworks.com/help/optim/ug/fsolve.html#buta__s-options

MaxFunctionEvaluations

Also we recommend against using global. See http://www.mathworks.com/help/matlab/math/parameterizing-functions.html

[Bassem Essam]

thanks for your concern, I will remove global but this is my 1st time using matlab, so... any tips wtih the options?

[Walter Roberson]

format long g

L2= 4.42;
X = 4+1i; t2 = 100*pi/180 + 1i; t1 = 50*pi/180 + 1i; h=0.5; %initial values%

options = optimoptions(@fsolve, 'MaxFunctionEvaluations', 10000, 'MaxIterations', 10000);
x= fsolve(@(x)SiccorLift(x,L2), [X;t2;t1;h], options);

Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.

X= x(1); t2= x(2)*180/pi; t1= x(3)*180/pi; h= x(4);

disp(X)

       2.96133921023046e-11 +      1.55828966080547i

disp(t2)

           90.0000000007112 +      31.2519208822566i

disp(t1)

           90.0000000002143 +      11.0910318354747i

disp(h)

           8.15035377555743 -  1.20326062635646e-12i

function F= SiccorLift(x, L2)
F(1) = x(1) + L2*cos(x(2)) - 5*cos(x(3));
F(2) = L2*sin(x(2))- 5*sin(x(3));
F(3)= x(1)+ 8*cos(x(3));
F(4)= 8*sin(x(3)) - x(4);
end

You can get exact solutions; MATLAB thinks there are four of them, whereas Maple says there are two solutions.

... Yes, this does mean that the complex results are not accidents: the exact solutions are complex-valued.