Pleas, what is wrong in this program?

proj()

Error using bvp4c (line 196)
Unable to solve the collocation equations -- a singular Jacobian encountered.

Error in solution>proj (line 17)
sol= bvp4c(@projfun,@projbc,solinit,options);
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

function sol= proj
myLegend1 = {};
k0=386; ce=3.831*10^2; mu=38.6*10^9;alfat=1.78*10^-5; rho=89.54*10^2; lamda=77.6*10^9;taw=0.5;Tnot=2.93*10^2;
c0=sqrt((lamda+2*mu)/(rho)); Betanot=(3*lamda+2*mu)*alfat; a1=mu/(lamda+2*mu);a2=(mu+lamda)/(lamda+2*mu);a3=(Betanot*Tnot)/(lamda+2*mu);omega=(rho*ce)/(k0);
a4=lamda/(lamda+2*mu);a5=(k0*omega*c0^2)/(k0);a6=(rho*ce*c0^2)/(k0);
a7=(Betanot*c0^2)/(k0); a8=a6*taw; a9=a7*taw; a10=rho*ce*taw*omega*c0^4/(k0); a11=Betanot*taw*omega*c0^4/(k0);w=rho*ce/(k0);
b34 = 1;
rr = [0.2 0.4 0.6];
for i =1:numel(rr)
    a= rr(i);
    s=1;h=1;
    y0 = [1,0,0,1,1,0,0];
    options =bvpset('stats','on','RelTol',1e-4);
    m = linspace(0,5);
    solinit = bvpinit(m,y0);
    sol= bvp4c(@projfun,@projbc,solinit,options);
    figure(1)
    plot(sol.x,(sol.y(5,:)))
    grid on,hold on
    myLegend1{i}=['alfa= ',num2str(rr(i))];
    
end
figure(1)
legend(myLegend1)
hold on
    function dy = projfun(x,y)
        dy = zeros(7,1);
        v = y(1);
        dv = y(2);
        u = y(3);
        du = y(4);
        t = y(5);
        dt = y(6);
        ddt = y(7);
        dy(1) = dv;
        dy(2)=(1/((((s^2+a1*h^2-(2*x+2+1).^2)*(1-a*t))*((h^2+a1*s^2-(2*(x+1+1)).^2)*(1-a*t)))-((a2*s*h)*(1-a*t))^2))*(((a2*s*h*a*2*(x+1)+2*(x+1)*a*a2*s*h)*t-a2*s*h*a*2*(x+1)*t^2-a2*s*h*2*(x+1)+(a*a2*s*h*a*(s^2+a1*h^2)*t-a2*s*h*a*(s^2+a1*h^2))*dt)*du+((s^2+a1*h^2-2*(x+1))*a*(h^2+a1*s^2)-(a*2*(x+1)*a*(a4*s*h+a1*s*h))+((a*a2*s*h)*a*(a4*s*h+a1*s*h)-(a*(s^2+a1*h^2-2*(x+1)))*(a*(h^2+a1*s^2))))*dt*dv+(a2*s*h*2*a*a3*s+a3*s*a*a2*s*h+2*a*a3*h*(s^2+a1*h^2-4*(x+1+1)^2)+a*(s^2+a1*h^2-(2*(x+1+1))^2)*(a3*h))*t*dt-(a2*s*h*a3*s)*dt-((s^2+a1*h^2-(2*(x+1))^2)*a3*h)*dt-dt*t^2*(a*a2*s*h*2*a*a3*s+a*(s^2+a1*h^2-(2*(x+1))^2)*2*a*a3*h));
        dy(3)=du;
        dy(4) =(1/(a*(s^2+a1*h^2-(2*x+2+1).^2)-(s^2+a1*h^2-(2*x+2+1).^2)))*((a2*s*h-a*a2*s*h*t)*((1/((((s^2+a1*h^2-(2*x+2+1).^2)*(1-a*t))*((h^2+a1*s^2-(2*(x+1+1)).^2)*(1-a*t)))-((a2*s*h)*(1-a*t))^2))*(((a2*s*h*a*2*(x+1)+2*(x+1)*a*a2*s*h)*t-a2*s*h*a*2*(x+1)*t^2-a2*s*h*2*(x+1)+(a*a2*s*h*a*(s^2+a1*h^2)*t-a2*s*h*a*(s^2+a1*h^2))*dt)*du+((s^2+a1*h^2-2*(x+1))*a*(h^2+a1*s^2)-(a*2*(x+1)*a*(a4*s*h+a1*s*h))+((a*a2*s*h)*a*(a4*s*h+a1*s*h)-(a*(s^2+a1*h^2-2*(x+1)))*(a*(h^2+a1*s^2))))*dt*dv+(a2*s*h*2*a*a3*s+a3*s*a*a2*s*h+2*a*a3*h*(s^2+a1*h^2-4*(x+1+1)^2)+a*(s^2+a1*h^2-(2*(x+1+1))^2)*(a3*h))*t*dt-(a2*s*h*a3*s)*dt-((s^2+a1*h^2-(2*(x+1))^2)*a3*h)*dt-dt*t^2*(a*a2*s*h*2*a*a3*s+a*(s^2+a1*h^2-(2*(x+1))^2)*2*a*a3*h)))+(((a*2*(x+1)*t)-2*(x+1)-(a*s^2+a*a1*h^2)*t)*du)+(2*a*a3*s*t-a3*s)*dt-(a*a4*s*h+a*a1*s*h)*dt*dv);
        dy(5)=dt;
        dy(6)=ddt;
        dy(7)=(1/(a*(a5*s^2*2*(x+1+1)+a5*h^2*2*(x+1+1))*t-(a5*s^2*2*(x+1+1)+a5*h^2*2*(x+1)-a8*(2*(x+1+1))^3)))*((s^2+h^2+2*a5*(s*2+2*h)-a6*(2*(x+1)+1).^2-3*a8*(2*(x+1)+1)*2*(x+1))*ddt-2*a6*(x+1)*dt-((1/(a*(s^2+a1*h^2-(2*x+2+1).^2)-(s^2+a1*h^2-(2*x+2+1).^2)))*((a2*s*h-a*a2*s*h*t)*((1/((((s^2+a1*h^2-(2*x+2+1).^2)*(1-a*t))*((h^2+a1*s^2-(2*(x+1+1)).^2)*(1-a*t)))-((a2*s*h)*(1-a*t))^2))*(((a2*s*h*a*2*(x+1)+2*(x+1)*a*a2*s*h)*t-a2*s*h*a*2*(x+1)*t^2-a2*s*h*2*(x+1)+(a*a2*s*h*a*(s^2+a1*h^2)*t-a2*s*h*a*(s^2+a1*h^2))*dt)*du+((s^2+a1*h^2-2*(x+1))*a*(h^2+a1*s^2)-(a*2*(x+1)*a*(a4*s*h+a1*s*h))+((a*a2*s*h)*a*(a4*s*h+a1*s*h)-(a*(s^2+a1*h^2-2*(x+1)))*(a*(h^2+a1*s^2))))*dt*dv+(a2*s*h*2*a*a3*s+a3*s*a*a2*s*h+2*a*a3*h*(s^2+a1*h^2-4*(x+1+1)^2)+a*(s^2+a1*h^2-(2*(x+1+1))^2)*(a3*h))*t*dt-(a2*s*h*a3*s)*dt-((s^2+a1*h^2-(2*(x+1))^2)*a3*h)*dt-dt*t^2*(a*a2*s*h*2*a*a3*s+a*(s^2+a1*h^2-(2*(x+1))^2)*2*a*a3*h)))+(((a*2*(x+1)*t)-2*(x+1)-(a*s^2+a*a1*h^2)*t)*du)+(2*a*a3*s*t-a3*s)*dt-(a*a4*s*h+a*a1*s*h)*dt*dv))*(a7*2*(s*(x+1)+2*(2*(x+1)+1)*2*(x+1))+6*a9*(2*(x+1)+1)^2)+du*(2+2*a*a11)-(6*a9*(2*(x+1)+1)-a*a11*(h*2*(x+1)+4*(1+2*(x+1)))+a7*(h*2*(x+1)+4*(2*(x+1)+1)))*((1/((((s^2+a1*h^2-(2*x+2+1).^2)*(1-a*t))*((h^2+a1*s^2-(2*(x+1+1)).^2)*(1-a*t)))-((a2*s*h)*(1-a*t))^2))*(((a2*s*h*a*2*(x+1)+2*(x+1)*a*a2*s*h)*t-a2*s*h*a*2*(x+1)*t^2-a2*s*h*2*(x+1)+(a*a2*s*h*a*(s^2+a1*h^2)*t-a2*s*h*a*(s^2+a1*h^2))*dt)*du+((s^2+a1*h^2-2*(x+1))*a*(h^2+a1*s^2)-(a*2*(x+1)*a*(a4*s*h+a1*s*h))+((a*a2*s*h)*a*(a4*s*h+a1*s*h)-(a*(s^2+a1*h^2-2*(x+1)))*(a*(h^2+a1*s^2))))*dt*dv+(a2*s*h*2*a*a3*s+a3*s*a*a2*s*h+2*a*a3*h*(s^2+a1*h^2-4*(x+1+1)^2)+a*(s^2+a1*h^2-(2*(x+1+1))^2)*(a3*h))*t*dt-(a2*s*h*a3*s)*dt-((s^2+a1*h^2-(2*(x+1))^2)*a3*h)*dt-dt*t^2*(a*a2*s*h*2*a*a3*s+a*(s^2+a1*h^2-(2*(x+1))^2)*2*a*a3*h))-(2*(a7+a9-a*a11))*dv)-(a*(s^2+h^2+4*a5-a6*(1+2*(x+1))^2-6*a8*(1+2*(x+1))*(x+1)))*t*ddt+(a*a6*2*(x+1))*t*dt+(a*(6*a9*(1+2*(x+1))+a9*12*(x+1)+8*a7*(x+1)+a7*s*(2*(x+1))))*t*((1/(a*(s^2+a1*h^2-(2*x+2+1).^2)-(s^2+a1*h^2-(2*x+2+1).^2)))*((a2*s*h-a*a2*s*h*t)*((1/((((s^2+a1*h^2-(2*x+2+1).^2)*(1-a*t))*((h^2+a1*s^2-(2*(x+1+1)).^2)*(1-a*t)))-((a2*s*h)*(1-a*t))^2))*(((a2*s*h*a*2*(x+1)+2*(x+1)*a*a2*s*h)*t-a2*s*h*a*2*(x+1)*t^2-a2*s*h*2*(x+1)+(a*a2*s*h*a*(s^2+a1*h^2)*t-a2*s*h*a*(s^2+a1*h^2))*dt)*du+((s^2+a1*h^2-2*(x+1))*a*(h^2+a1*s^2)-(a*2*(x+1)*a*(a4*s*h+a1*s*h))+((a*a2*s*h)*a*(a4*s*h+a1*s*h)-(a*(s^2+a1*h^2-2*(x+1)))*(a*(h^2+a1*s^2))))*dt*dv+(a2*s*h*2*a*a3*s+a3*s*a*a2*s*h+2*a*a3*h*(s^2+a1*h^2-4*(x+1+1)^2)+a*(s^2+a1*h^2-(2*(x+1+1))^2)*(a3*h))*t*dt-(a2*s*h*a3*s)*dt-((s^2+a1*h^2-(2*(x+1))^2)*a3*h)*dt-dt*t^2*(a*a2*s*h*2*a*a3*s+a*(s^2+a1*h^2-(2*(x+1))^2)*2*a*a3*h)))+(((a*2*(x+1)*t)-2*(x+1)-(a*s^2+a*a1*h^2)*t)*du)+(2*a*a3*s*t-a3*s)*dt-(a*a4*s*h+a*a1*s*h)*dt*dv))+b34*t*du+(a*(a7*(h*2*(x+1)+2*2*((1+2*(x+1))))+3*a9*2*(x+1)+3*a9*2*((1+2*(x+1)))))*t*((1/((((s^2+a1*h^2-(2*x+2+1).^2)*(1-a*t))*((h^2+a1*s^2-(2*(x+1+1)).^2)*(1-a*t)))-((a2*s*h)*(1-a*t))^2))*(((a2*s*h*a*2*(x+1)+2*(x+1)*a*a2*s*h)*t-a2*s*h*a*2*(x+1)*t^2-a2*s*h*2*(x+1)+(a*a2*s*h*a*(s^2+a1*h^2)*t-a2*s*h*a*(s^2+a1*h^2))*dt)*du+((s^2+a1*h^2-2*(x+1))*a*(h^2+a1*s^2)-(a*2*(x+1)*a*(a4*s*h+a1*s*h))+((a*a2*s*h)*a*(a4*s*h+a1*s*h)-(a*(s^2+a1*h^2-2*(x+1)))*(a*(h^2+a1*s^2))))*dt*dv+(a2*s*h*2*a*a3*s+a3*s*a*a2*s*h+2*a*a3*h*(s^2+a1*h^2-4*(x+1+1)^2)+a*(s^2+a1*h^2-(2*(x+1+1))^2)*(a3*h))*t*dt-(a2*s*h*a3*s)*dt-((s^2+a1*h^2-(2*(x+1))^2)*a3*h)*dt-dt*t^2*(a*a2*s*h*2*a*a3*s+a*(s^2+a1*h^2-(2*(x+1))^2)*2*a*a3*h)))+(a*a7*2)*t*dv-(a*(s^2+h^2+a5*s*2+a5*h*2+a10*2*(x+1)*((1+2*(x+1)))))*(dt*dt)-(a*a5*(1+2*(x+1))*(s^2+h^2)+a*a10*(1+2*(x+1))^3)*dt*ddt);
    end
    function res = projbc(ya,yb)
        res = [ya(1);
            ya(3);
            ya(5);
            ya(7);
            yb(1);
            yb(3);
            yb(5);
            ];
    end
end

[Torsten]

b34 is undefined and you use "a8(" instead of "a8*("

[T K]

@ Torsten: Pleas make b34=1 and correct the muliplication product with a8, can you run this program?

[Torsten]

can you run this program?

No - I get an error (see above).

[Harald]

Hi,

please check this answer and the one linked:

https://de.mathworks.com/matlabcentral/answers/812985-bvp4c-unable-to-solve-the-collocation-equations-a-singular-jacobian-encountered

Best wishes,

Harald