Singular Jacobian using bvp4c

I know similar questions have been asked, but I am wondering if there any tricks to help out here. I've tried changing variables, but the divergence just moves around...

I am trying to solve a second order equation, given in the screen shot below, and the associated code is attached:

I did not impose the condition f>=0, so maybe that is my issue? The hyperbolic tanh might also be a good initial guess, but I was relying on the Sxint = deval() to get me started. Any obvious problems? Thanks in advanced for any help!

xl = 0;
xr = 10;
[Sxint, xint] =bvp4c_mathworks_Abrikosov(xl,xr);

Error using bvp4c
Unable to solve the collocation equations -- a singular Jacobian encountered.

Error in solution>bvp4c_mathworks_Abrikosov (line 13)
sol = bvp4c(@myode,@mybc,solinit);

plot(xint,Sxint)

function [Sxint, xint] =bvp4c_mathworks_Abrikosov(xl,xr)

N = 500;                           

xint = linspace(xl,xr,N);

solinit = bvpinit(xint,[0 0]);        
sol = bvp4c(@myode,@mybc,solinit);

Sxint = deval(sol,xint);
end

function dy = myode(r,y)
k = 1/sqrt(1.8);
dy(1,1) = y(2);
dy(2,1) = k^2*(y(1)^2-1)*y(1)+y(1)/r^2-y(2)/r;
end

function res = mybc(ya,yb)
res = [ya(1)
      yb(1)-1];
end

Answer 1

[Neelanshu]

Hello Marcus,

I understand that you're encountering the "Singular Jacobian using bvp4c" error while attempting to solve a boundary value problem.

Upon inspecting the code, it appears that the issue arises when the function 'myode' is called with the value of 'r' being zero, as shown:

This results in the computation of 'dy(2,1)' to be 'NaN' because it involves division of zero by zero, which leads to the error you're experiencing. To rectify this, you should either initialize 'r' with a non-zero value or adjust the formula used to compute 'dy(2,1)' to handle the case when 'r' is zero.

Hope this helps.