Using fsolve in for loop for find solutions to equation

for example if i have next functions: (which i need solving in the same time in a for loop for different t12)

    x2=C*((sin(x2+x1*sinh(t12))))/(tg((x2+x1*cos(t12)))));
    x1=C*(sin((x1+x2*sinh(t12)))))/(tg((x1+x2*cos(t12)))); 

(C- just constant lets say it equal 1)

t12- i change every loop lets say it linspace(-pi, pi)

so i tried to do it like this:

tt12=linspace(-pi, pi);  %angle changing
C=1; %just constant
x1_vec=zeros(1,length(tt12)); x2_vec=zeros(1,length(tt12)) % vector in which i collect sollutions

x1=rand; x2=rand; % initial conditions

for i=1:length(tt12)
    t12=tt12(i);
    F= @(V)  [ V(1)-C*sin(V(1)+V(2)*sinh(t12))/(tan(V(1)+V(2)*cos(t12)));
        V(2)-C*sin(V(2)+V(1)*sinh(t12))/(tan(V(2)+V(1)*cos(t12)));
        ];
    InitialGuess=[x1;x2];
  
    XY = fsolve(F, InitialGuess);
    x1=XY(1);
    x2=XY(2);
    x1_vec(i)=x1;
    x2_vec(i)=x2;
end

but every loop i get the next message which make it really slow: (since every loop it print it!)

what should i do so it will work faster (with no such printing (since i want to use t12 vector of lets say 80000 and then it will be too long if it prints every loop and calculation) ?

Best regards,

Answer 1

[Stephan]

Add this line before you call fsolve

options = optimoptions('fsolve','Display','off');

and then call fsolve with this options:

XY = fsolve(F, InitialGuess, options);

[Litalo]

Hi thanks, but somhow my code stuck (its much longer vector t12 than what i wrote in the example), does it is in general slower to solve an equation in for loop than just for example do simple integration in time?

Best,

Lital

[Stephan]

You could try to work with parfor.