MATLAB: How to solve nonlinear equations using boundary conditions

fsolveMATLABnonlinear equationnumerical solution

Hi all,
I have two sets of equation.
 m_c_theta0=(m_c0-1/M+1)*cos(theta0)+j_L0*sin(theta0)+1/M-1;
j_L_theta0=(-m_c0+1/M-1)*sin(theta0)+j_L0*cos(theta0);
j_M0=j_L_theta0-l*theta0;
m_m_theta0=1;
m_c_gama=(m_c_theta0-1/M-1)*cos(gama-theta0)... 
          +j_L_theta0*sin(gama-theta0)+1/M+1;
j_L_gama=(-m_c_theta0+1/M+1)*sin(gama-theta0) ...
          +j_L_theta0*cos(gama-theta0);
j_M_gama=j_L_theta0-l*(gama-theta0);
m_m_gama=-1;
boundary conditions are
    [ j_L_gama+x(1); %curernt
             m_c_gama+x(2); %voltage
             j_M0+j_M_gama; 
          m_m_theta0+1;      
            ];
where,
     l=0.2, F=0.5:0.1:1.5; gama=pi/F;
I need to find the initial,
j_L0=x(1);
m_c0=x(2);
theta0=x(3);
M=x(4);
for above F range and plot(F,M)
I want to do it by using fsolve.
can anyone please help?

Best Answer

options=optimset('Display','on',...
    'Algorithm','trust-region-reflective','LargeScale','off','MaxFunEvals',20000);   
l=0.4; 
Fvals = 0.5:0.1:1.5;
numF = length(Fvals);
j_L0 = zeros(1, numF);
m_c0 = zeros(1, numF);
theta0 = zeros(1, numF);
M = zeros(1,numF);
for F_idx = 1 : numF
  F = Fvals(F_idx);
  func_CC=@(x)myfun_CC(x,l,F);
  x0=[ 1, -1.5, 2 1]; % Make a starting guess at the solution
  x = fsolve(func_CC, x0, options);  % Call solver
  j_L0(F_idx) = x(1);
  m_c0(F_idx) = x(2);
  theta0(F_idx) = x(3);
  M(F_idx) = x(4);
end
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