Solve a second order BVP with a singularity problem

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Jacob Jepson 2020-3-23

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/512519-solve-a-second-order-bvp-with-a-singularity-problem

I am trying to use BVP4C to solve a second order nonlinear BVP. My code below includes the initial guess, boundary conditions etc. I think there is something wrong with the division by y(1) in the bvpfcn part, as without it there seems to be no problem running it. Could someone suggest a way to get round this? Even if I try the interval to be (-100,-1) there still seems to be a problem with not being able to meet the tolerance. Many thanks in advance!

xmesh = linspace(-100,0,500);
solinit = bvpinit(xmesh, @guess);
sol = bvp4c(@bvpfcn, @bcfcn, solinit);
plot(sol.x,sol.y(1,:),'k')
function dydx = bvpfcn(~,y) %The BVP problem
%dydx = zeros(2,1);
dydx = [y(2)
       (y(1)-1) - y(2)*(15+y(2))/y(1)]; %I think the problem is the division by y(1) here
end
function res = bcfcn(ya,yb) %Boundary conditions
res = [ya(2)
       yb(1)];
end
function g = guess(x) %Initial guess
g = [sin(x)
     cos(x)];
end