For loop inside functions in fsolve

Hello, I have 2 by 2 system of nonlinear equations.

I will use for loop for my time T inside these two functions.

I have this function for fsolve:

function F=torder1(x)

     x_1=[0:0.01:1];
     b=0.6;

dt = 0.01;
Nt = 1/dt+1;

%$ sol(1) = h; sol(2) =theta;
clear x_1;   
syms x_1 h theta kappa
f_1(x_1,h,theta,kappa) = 1/2*(1-( (h+(1-b)*theta)^2/(h+(x_1-b)*theta-kappa*x_1*(1-x_1))^2 ));
f_2(x_1,h,theta,kappa) = (x_1-b)/2*( 1-( (h+(1-b)*theta)^2/(h+(x_1-b)*theta-kappa*x_1*(1-x_1))^2 ));
kappa =1;

f_11 = 1-( (h+(x_1-b)*theta)^2/(h+(x_1-b)*theta-1*x_1*(1-x_1))^2 );
f_21 = (x_1-b)/2*( 1-( (h+(1-b)*theta)^2/(h+(x_1-b)*theta-x_1*(1-x_1))^2 ));

fint_1 = int(f_11, x_1);
fint_2 = int(f_21, x_1);

x_1=1;
upper_1=subs(fint_1);
upper_2=subs(fint_2);
clear x_1;
x_1=0;
lower_1=subs(fint_1);
lower_2=subs(fint_2);
clear x_1;
integral_result_1old=upper_1-lower_1;
integral_result_2old=upper_2-lower_2;

h0 = kappa *b*(1-b);
theta0 = kappa*(1-2*b);

integral_result_1 = subs(integral_result_1old, {h, theta}, {x(1), x(2)});
integral_result_2 = subs(integral_result_2old, {h, theta}, {x(1), x(2)});
*for nt=1:Nt
    T(nt)=(nt-1)*dt;
F(nt)* = [double(x(1) - integral_result_1*T(nt)^2 -h0);
    double(x(2) - integral_result_2*T(nt)^2 - theta0)];
end

Also I have my script in which the function torder1.m is nested:

x0 = [.1, .1];
options = optimoptions('fsolve','Display','iter');
dt=0.01;
Nt=1/dt+1;

[x,fval] = fsolve(@torder1,x0,options)
h = x(1)
theta = x(2)

I have to loop over my time T (very bottom in the torder1.m function) and in every time step,

I need to get my x(1) = h and x(2) = theta and related F in every time and save them to plot against T.

The time index is shown as nt.

Thanks for any help.

Answer 1

[Qu Cao]

I recommend you to provide more details about the equations you want to solve.

You can also refer to the following documentation to see how to use 'fsolve':

http://www.mathworks.com/help/optim/ug/fsolve.html