unable to identify the error in my program so as to get my plots

function Maxw
global M la  Pr  Nb Nt W  Le ga A B 
infinity =10;
% M=0.5; S=0.2; Ld=0.3; R=0.6; N=0.3; Nb=0.5; Nt=0.5; Pr=0.71; Ki=0.5; Le=1;
%  Bi=0.5; Ec=0.5; Ws=0.3;
 W= 0.3; M=0.1; la=0.5; Pr=0.71; A=0.1; B=0.1; Nt=0.5; Nb=0.5;  
  Le=0.1;ga=0.01;
 
 Ldva=[0.5 1.0 2.0 3.0];
 for i = 1:4
     Ld=Ldva(i);
     
     lines = {'b','r','g','c'};
     solinit = bvpinit(linspace(0,infinity),[0 1 1 la 1 0 0]);
      sol = bvp4c(@shootode,@shootbc,solinit);
      eta = sol.x;
      f = sol.y;
%       fprintf('Nt = %f\t,skin =%f\t, Nus=%f\t, shr=%f\n', M ,f(3,1),-f(5,1),-f(7,1));
%        fprintf('%f\t',f(3,1)+(1/2)*Ws*f(3,1)*f(3,1));
%         fprintf('%f\t',-f(5,1));
  %      fprintf('%f\t',-f(7,1));
      
% %     
    figure(1)   
    set(gca,'Fontsize',12);
   plot(eta,f(2,:), lines{i},'linewidth',1);
    xlabel('\eta');     
    ylabel('f ^{\prime}(\eta)');
    hold on

    
  
 end
%   hold on
% --------------------------------------------------------------------------

function dydx = shootode(eta,f)
%EX5OfE  ODE function for Example 5 of the BVP tutorial.  
global M Nb Nt Le Pr W A B la ga
dydx =  [
          f(2)
          f(3)
         (1/(1+W*f(3)))*(-f(1)*f(3)-f(2)^2+M*f(2)-la^2)
          f(5)
           (-(Pr*(f(1)*f(5)+Nb*f(5)*f(7)+Nt*f(5)*f(5)))-A*f(2)-B*f(4))
           f(7)
          (((Nt/Nb)*(Pr*(f(1)*f(5)+Nb*f(5)*f(7)+Nt*f(5)*f(5)))-A*f(2)-B*f(4))+ga*Le*f(6)+Le*f(1)*f(7))];

             
  % --------------------------------------------------------------------------

function res = shootbc(fa,fb)
%EX5BC  Bounfarf conditions for Example 5 of the BVP tutorial.
global la
res = [ fa(1)-0
         fa(2)-1
         fa(4)-1
         fa(6)-1
         fb(2)-la
         fb(4)-0
         fb(6)-0
        ];

Answer 1

[Walter Roberson]

Maxw;

function Maxw
global M la  Pr  Nb Nt W  Le ga A B 
infinity =10;
% M=0.5; S=0.2; Ld=0.3; R=0.6; N=0.3; Nb=0.5; Nt=0.5; Pr=0.71; Ki=0.5; Le=1;
%  Bi=0.5; Ec=0.5; Ws=0.3;
 W= 0.3; M=0.1; la=0.5; Pr=0.71; A=0.1; B=0.1; Nt=0.5; Nb=0.5;  
  Le=0.1;ga=0.01;
 
 Ldva=[0.5 1.0 2.0 3.0];
 
 options = bvpset('NMax', 1e6);
 
 for i = 1:4
     fprintf('starting iter %d\n', i);
     Ld=Ldva(i);
     
     lines = {'b','r','g','c'};
     solinit = bvpinit(linspace(0,infinity),[0 1 1 la 1 0 0]);
      sol = bvp4c(@shootode,@shootbc,solinit, options);
      eta = sol.x;
      f = sol.y;
%       fprintf('Nt = %f\t,skin =%f\t, Nus=%f\t, shr=%f\n', M ,f(3,1),-f(5,1),-f(7,1));
%        fprintf('%f\t',f(3,1)+(1/2)*Ws*f(3,1)*f(3,1));
%         fprintf('%f\t',-f(5,1));
  %      fprintf('%f\t',-f(7,1));
      
% %     
    figure(1)   
    set(gca,'Fontsize',12);
   plot(eta,f(2,:), lines{i},'linewidth',1);
    xlabel('\eta');     
    ylabel('f ^{\prime}(\eta)');
    hold on
    fprintf('done iter %d\n', i);
    
  
 end
end
%   hold on
% --------------------------------------------------------------------------


function dydx = shootode(eta,f)
%EX5OfE  ODE function for Example 5 of the BVP tutorial.  
global M Nb Nt Le Pr W A B la ga
dydx =  [
          f(2)
          f(3)
         (1/(1+W*f(3)))*(-f(1)*f(3)-f(2)^2+M*f(2)-la^2)
          f(5)
           (-(Pr*(f(1)*f(5)+Nb*f(5)*f(7)+Nt*f(5)*f(5)))-A*f(2)-B*f(4))
           f(7)
          (((Nt/Nb)*(Pr*(f(1)*f(5)+Nb*f(5)*f(7)+Nt*f(5)*f(5)))-A*f(2)-B*f(4))+ga*Le*f(6)+Le*f(1)*f(7))];

             
  % --------------------------------------------------------------------------
end

function res = shootbc(fa,fb)
%EX5BC  Bounfarf conditions for Example 5 of the BVP tutorial.
global la
res = [ fa(1)-0
         fa(2)-1
         fa(4)-1
         fa(6)-1
         fb(2)-la
         fb(4)-0
         fb(6)-0
        ];
end

On MATLAB Online, the result is:

starting iter 1

Error using bvp4c (line 251)

Unable to solve the collocation equations -- a singular Jacobian encountered.

Error in q738457>Maxw (line 21)

sol = bvp4c(@shootode,@shootbc,solinit, options);

Error in q738457 (line 1)

Maxw;

Note: When I did not the options configured, it was complaining about the number of mesh points needing to be larger.

[alfunsa Prathia]

Thank you But still my doubt is not clear can you please explain

[Walter Roberson]

https://www.mathworks.com/matlabcentral/answers/120468-why-do-i-receive-an-error-about-a-singular-jacobian-when-i-use-the-bvp4c-function-within-matlab

[Walter Roberson]

Eventually the code ends up doing an LU decomposition on a Jocobian matrix of size 18487, but the rank of the L component turns out to be only 18473 . So this is not a case of the jacobian "slipping" into singular due to simple round-off problems with one row: 14 of the rows become redundant. That is not even 1 in 1000, but it is enough.