can anyone help me. I am getting error of the following problem

bb_go

b = 0.2000

R = 0.5000

M = 0.2000

L = 2

Error using bvp4c (line 196)
Unable to solve the collocation equations -- a singular Jacobian encountered.

Error in solution>bb_go (line 7)
sol = bvp4c(@bvp2D,@bc2D,sol1);
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

function [y]=bb_go
% defining parameters
b=0.2,R=0.5,M=0.2,L=2, Pr=0.4;
sol1   = bvpinit(linspace(0,3,5),[1 0 1 0 1]);
    sol    = bvp4c(@bvp2D,@bc2D,sol1);
    x      = sol.x;
    y      = sol.y; 
 
    %%% Plotting of the velocity
    figure (1)
    plot(x, y(2, :) ,'linewidth', 1)
    hold on
    xlabel('\eta', 'fontweight', 'bold', 'fontsize', 16)
    ylabel('f^/(\eta)', 'fontweight', 'bold', 'fontsize', 16)
   
    %% Residual of the boundary conditions
  function residual = bc2D(y0, yinf)         
     residual=[y0(1);  y0(2); y0(3)-1; yinf(2); yinf(3)];      
  end

   %%  System of First Order ODEs
  function yvector = bvp2D(t,y)
        yy1 = (1/(1+1/b))*(M*y(2)-y(1)*y(3)-L*(1-y(2)*y(2)));
        yy2=(1/(1+R))*Pr*(y(2)*y(3)-y(1)*y(4));
      yvector  = [y(2);y(3);y(4);yy1;yy2];
  end
end

[Chuguang Pan]

What is the dimension of state vector y, it seems that the dimension of y is 4 but the yvector is 5.

Answer 1

[Torsten]

Let's ignore the fifth differential equation in your code for a moment.

Then you set up code for the differential equation

y'''' = 1/(1+1/b) * (M*y' - y*y'' - L*(1-y'^2))

What are the four boundary conditions you want to impose for this equation (thus most probably 4 out of the 5 you set in your code) ?

residual=[y0(1);  y0(2); y0(3)-1; yinf(2); yinf(3)];

After you've selected these 4, the fifth differential equation needs a condition that involves y(5), either at x=0 or x=Inf.

[Saswati]

thank u..i got it.