MATLAB: 4 non linear simultaneous equations

equationfsolvesimultaneoussolver

I have the following 4 questions and want to solve them using fsolve
F(1)=x(1)+x(3)-12.54;
F(2)=x(2)+x(4)-12.245;
F(3)= 2*x(1)+n(2)+n(3)-(1493/60);
F(4) =(x(3)*x(2))/(x(1)*x(4))-1000;

Best Answer

Hi Misha
this is John BG <mailto:jgb2012@sky.com jgb2012@sky.com>
1.
define the function to solve with in for instance a separate file
function F=fun1(x,n)
F(1)=x(1)+x(3)-12.54; 
F(2)=x(2)+x(4)-12.245; 
F(3)= 2*x(1)+n(2)+n(3)-(1493/60); 
F(4) =(x(3)*x(2))/(x(1)*x(4))-1000;
2.
if choosing a single lucky start point, then for instance
f1=@fun1
x0=[1 1 1 1];
n=[1 2 1 2];
options = optimoptions('fsolve','Display','none','PlotFcn',@optimplotfirstorderopt);
f2=@(x) f1(x,n)
Y=fsolve(f2,x0)
 Y =
     2.9951    4.5133    1.6388    0.0025
3.
Not all start points allow fsolve to start, for instance starting x0 all nulls fsolve returns error
x0=[0 0 0 0];
Y=fsolve(f2,x0)
 Error using trustnleqn (line 28)
 Objective function is returning undefined values at initial point. FSOLVE cannot continue.
   Error in fsolve (line 388)
           trustnleqn(funfcn,x,verbosity,gradflag,options,defaultopt,f,JAC,...
4.
A way to understand that there are multiple real roots is changing fsolve options to
.
problem.options = optimoptions('fsolve','Display','none','PlotFcn',@optimplotfirstorderopt);
problem.objective = f2;
problem.x0 = [1 1 1 1];
problem.solver = 'fsolve';
Y=fsolve(problem)
grid on
.
.
Misha, if you find this answer useful would you please consider marking my answer as Accepted Answer?
To any other reader, if you find this answer useful please consider clicking on the thumbs-up vote link
thanks in advance
John BG
<mailto:jgb2012@sky.com jgb2012@sky.com>
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