MATLAB: How to solve this bvp4c error

bvp4c

So, the error I am getting is : "Unable to solve the collocation equations — a singular Jacobian encountered" When ever I change "K" value of the global variable to 0, and also the error : Error in Comparison sol = bvp4c(@rhs_bvp, @bc_bvp, init);
The highest order is 2 in the equation :
And the equation is subjected to the boundary value: y = 0 at x = -1 and y = 1 at x = 1 
global  G m M Da k e1 e2 Uhs  beta n gamma
M = 2; m = 0.1; Da = 0.1; Uhs = 1; e1 = 2; e2 = 2; G = 1; k = 0; beta = 0.025;
n = 0; gamma = 0.25;
    
    init = bvpinit (linspace(-1,1),[1 0]);
    sol = bvp4c(@rhs_bvp, @bc_bvp, init);
    yplot =sol.y(1,:);
    xplot =sol.x;
    plot(xplot,yplot)
function rhs = rhs_bvp(x,y)
global  G m M Da k e1 e2 Uhs gamma n
vel = (((M^2/(1+(m^2))+(1/Da))*y(1)) - G - ((k^2)*Uhs)*((( (e1+e2)/(2*cosh(k))*cosh(k*x) ) - (((e1- e2)/(2*sinh(k)))*sinh(k*x)))))/((1-n)+((sqrt(2))*n*gamma*y(2)));
rhs = [ y(2)
    vel
      
    ];
end
function bc = bc_bvp(yl,yr)
bc = [yl(1)
    yr(1)-1
    ];
end
Could the error be in the initial value of the problem ?

Best Answer

You have a division by sinh(k)
.../(2*sinh(k)))...
Since k is zero, sinh(k) is zero and the resuting expression for vel is NaN.
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