Error using bvp4c (singular jacobian encountered)

How can I find the error in this MATLAB's script?

Script one: perfiles_thiele

clc; clear;
R=3;%input('Radio de particula en mm, R: ');
%%BVP solution problem
C0=2E-4;
dCdr0=0.016;
solinit = bvpinit(linspace(0,R,100),[C0 dCdr0]); 
sol = bvp4c(@model,@ex1bc,solinit);

   r =sol.x;
   C=sol.y(1,:);
   v=sol.y(2,:);

TWO:

function F =model(r,Y)

R=3;
Thiele =1;

   C=Y(1);
   v=Y(2);

dCdr= v;      
dvdr= (-2/r)*v + C*9*Thiele^2/R^2;
F = [dCdr; dvdr];
end

THREE:

function res = ex1bc(ya,yb) 

Cs=2E-6;
dCdr=0;

res = [ ya(1) - Cs 
        yb(2) - dCdr];
end

When I run the script one throws me the error:

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

Error in perfiles_thiele (line 19)
 sol = bvp4c(@model,@ex1bc,solinit);

I appreciate help to know if the problem is the definition of [C0 dCdr0] or if it is because I have some error in my BVP system.

Thanks!

[Walter Roberson]

As we only have your code and not your equations, we cannot compare to determine if there is a problem.

Answer 1

[Torsten]

Don't start at r = 0, but at r = a small number.

Best wishes

Torsten.

Answer 2

[CLMSP]

Clear! thank you!

[MOSLI KARIM]

%%

function solved

clc; clear;

global Thiele Cs R C0 dCdr0

Cs=2E-6

Thiele =1

R=3;%input('Radio de particula en mm, R: ');

%%BVP solution problem

C0=2E-4;

dCdr0=0.016;

solinit = bvpinit(linspace(0.01,R,100),[C0 dCdr0]);

sol = bvp4c(@model,@ex1bc,solinit);

RR=sol.x'

display(RR)

C=sol.y(1,:);

v=sol.y(2,:);

figure(1)

plot(RR,C)

figure(2)

plot(RR,v)

function F =model(r,Y)

C=Y(1);

v=Y(2);

dCdr= v;

dvdr= (-2/r)*v + C*9*Thiele^2/R^2;

F = [dCdr; dvdr];

end

function res = ex1bc(ya,yb)

res = [ ya(1) - Cs

yb(2) ];

end

end

[MOSLI KARIM]

your code works well, I just made x=a=0.001 to avoid the singularity