Error using bvp4c (singular jacobian encountered)

Hi, I got error while running this problem of bvp. What does this mean and how to solve this?

Error:

Error using bvp4c (line 251)
Unable to solve the collocation equations -- a singular Jacobian encountered

Here is the code:

function ex111bvp
n=1;
solinit = bvpinit(linspace(0,20,2),[0 0 0 0 -1]);
options = bvpset('Stats','on','RelTol',1e-5);
sol = bvp4c(@ex111ode,@ex111bc,solinit,options);
% The solution at the mesh points
x = sol.x;
y = sol.y;
figure
plot(x,y')
title('Example 111')
ylabel('sol')
xlabel('eta')
% --------------------------------------------------------------------------
function dydx = ex111ode(x,y,n)
n=1;
dydx =  [ -2*y(3)-x*(1-n/(n+1))*y(4)
        y(3)
        y(2)^2-(y(4)+1)^2+(y(1)+(1-n/(n+1))*x*y(2))*y(3)-y(3)*(n-1)*(y(3)^2+y(5)^2)^((n-3)/2)*y(5)*(((y(3)^2+y(5)^2)^((n-1)/2)+y(3)^2*(y(3)^2+y(5)^2)^((n-3)/2)*(n-1))*((y(3)^2+y(5)^2)^((n-1)/2)+y(5)^2*(y(3)^2+y(5)^2)^((n-3)/2)*(n-1))-((y(3)^2+y(5)^2)^((n-1)/2)+y(5)^2*(y(3)^2+y(5)^2)^((n-3)/2)*(n-1))*(y(3)*(y(1)-x*y(2)*(1-n/(n+1)))-(y(4)+1)^2+y(2))+((y(3)^2+y(5)^2)^(3-n)*(y(3)^2+y(5)^2)^((n-3)/2)*(y(5)*(y(1)-x*y(2)*(1-n/(n+1)))-2*y(2)*(y(4)+1)))/(y(3)*y(5)*(n-1)))/(((y(3)^2+y(5)^2)^((n-1)/2)+y(3)*(n-1)*(y(3)^2+y(5)^2)^((n-3)/2))) 
        y(5)
        -2*y(2)*(y(4)+1)+(y(1)-x*(1-n/(n+1))*y(2))*y(5)-y(5)*(n-1)*(y(3)^2+y(5)^2)^((n-3)/2)*y(3)*(y(3)*y(5)*(y(3)^2+y(5)^2)^((n-3)/2)*(n-1)*(y(3)*(y(1)-x*y(2)*(1-n/(n+1)))-(y(4)+1)^2+y(2))-((y(3)^2+y(5)^2)^((n-1)/2)+y(3)^2*(y(3)^2+y(5)^2)^((n-3)/2)*(n-1))*((y(3)^2+y(5)^2)^((n-1)/2)+y(5)*(y(3)^2+y(5)^2)^((n-1)/2)+y(5)*(y(3)^2+y(5)^2)^((n-3)/2)*(n-1))-((y(3)^2+y(5)^2)^(3-n)*(y(5)*(y(1)*x*y(2)*(1-n/(n+1)))-2*y(2)*(y(4)+1))*((y(3)^2+y(5)^2)^((n-1)/2)+y(3)*(y(3)^2+y(5)^2)^((n-3)/2)*(n-1)))/(y(3)^2*y(5)^2*(n-1)^2))/(((y(3)^2+y(5)^2)^((n-1)/2)+y(5)*(n-1)*(y(3)^2+y(5)^2)^((n-3)/2))) ];
%-------------------------------------------------------------------------
function res = ex111bc(ya,yb)
res = [ ya(1)
      ya(2)
      ya(4)
      yb(2)
      yb(4)+1];
%-------------------------------------------------------------------------

Thank you in advance.

Answer 1

[Torsten]

Use

sol = bvp4c(@(x,y)ex111ode(x,y,n),@ex111bc,solinit,options);

as call to bvp4c.

If the problem persists, look whether dydx contains Inf or NaN values.

Best wishes

Torsten.