How can i remove singular Jacobin error from this code?

Question

Sharqa on 12 Nov 2024

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Direct link to this question

https://nl.mathworks.com/matlabcentral/answers/2165719-how-can-i-remove-singular-jacobin-error-from-this-code

Answered: Sandeep Mishra on 25 Nov 2024 at 11:55

Open in MATLAB Online

william()

k2 = 40

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-33 * 0 0 NaN 0 -0.1807

dydx = 5×1

1.0e-13 * 0.1490 0 NaN 0 -0.0000

dydx = 5×1

1.0e-13 * 0 -0.1490 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-13 * 0 0 NaN 0.1490 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-33 * 0 0 NaN 0 -0.1807

dydx = 5×1

1.0e-13 * 0.1490 0 NaN 0 -0.0000

dydx = 5×1

1.0e-13 * 0 -0.1490 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-13 * 0 0 NaN 0.1490 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-33 * 0 NaN NaN 0 -0.1807

dydx = 5×1

1.0e-13 * -0.1490 NaN NaN 0 -0.0000

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-13 * 0 NaN NaN 0.1490 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-33 * 0 0 NaN 0 -0.1807

dydx = 5×1

1.0e-13 * 0.1490 0 NaN 0 -0.0000

dydx = 5×1

1.0e-13 * 0 -0.1490 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-13 * 0 0 NaN 0.1490 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-33 * 0 NaN NaN 0 -0.1807

dydx = 5×1

1.0e-13 * -0.1490 NaN NaN 0 -0.0000

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-13 * 0 NaN NaN 0.1490 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-33 * 0 0 NaN 0 -0.1807

dydx = 5×1

1.0e-13 * 0.1490 0 NaN 0 -0.0000

dydx = 5×1

1.0e-13 * 0 -0.1490 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-13 * 0 0 NaN 0.1490 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-33 * 0 NaN NaN 0 -0.1807

dydx = 5×1

1.0e-13 * -0.1490 NaN NaN 0 -0.0000

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-13 * 0 NaN NaN 0.1490 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-33 * 0 0 NaN 0 -0.1807

dydx = 5×1

1.0e-13 * 0.1490 0 NaN 0 -0.0000

dydx = 5×1

1.0e-13 * 0 -0.1490 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-13 * 0 0 NaN 0.1490 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-33 * 0 NaN NaN 0 -0.1807

dydx = 5×1

1.0e-13 * -0.1490 NaN NaN 0 -0.0000

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-13 * 0 NaN NaN 0.1490 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-33 * 0 0 NaN 0 -0.1807

dydx = 5×1

1.0e-13 * 0.1490 0 NaN 0 -0.0000

dydx = 5×1

1.0e-13 * 0 -0.1490 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-13 * 0 0 NaN 0.1490 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-33 * 0 NaN NaN 0 -0.1807

dydx = 5×1

1.0e-13 * -0.1490 NaN NaN 0 -0.0000

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-13 * 0 NaN NaN 0.1490 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-33 * 0 0 NaN 0 -0.1807

dydx = 5×1

1.0e-13 * 0.1490 0 NaN 0 -0.0000

dydx = 5×1

1.0e-13 * 0 -0.1490 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-13 * 0 0 NaN 0.1490 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-33 * 0 NaN NaN 0 -0.1807

dydx = 5×1

1.0e-13 * -0.1490 NaN NaN 0 -0.0000

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-13 * 0 NaN NaN 0.1490 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-33 * 0 0 NaN 0 -0.1807

dydx = 5×1

1.0e-13 * 0.1490 0 NaN 0 -0.0000

dydx = 5×1

1.0e-13 * 0 -0.1490 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-13 * 0 0 NaN 0.1490 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-33 * 0 NaN NaN 0 -0.1807

dydx = 5×1

1.0e-13 * -0.1490 NaN NaN 0 -0.0000

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-13 * 0 NaN NaN 0.1490 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-33 * 0 0 NaN 0 -0.1807

dydx = 5×1

1.0e-13 * 0.1490 0 NaN 0 -0.0000

dydx = 5×1

1.0e-13 * 0 -0.1490 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-13 * 0 0 NaN 0.1490 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-33 * 0 NaN NaN 0 -0.1807

dydx = 5×1

1.0e-13 * -0.1490 NaN NaN 0 -0.0000

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-13 * 0 NaN NaN 0.1490 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-33 * 0 0 NaN 0 -0.1807

dydx = 5×1

1.0e-13 * 0.1490 0 NaN 0 -0.0000

dydx = 5×1

1.0e-13 * 0 -0.1490 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-13 * 0 0 NaN 0.1490 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-33 * 0 NaN NaN 0 -0.1807

dydx = 5×1

1.0e-13 * -0.1490 NaN NaN 0 -0.0000

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-13 * 0 NaN NaN 0.1490 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-33 * 0 0 NaN 0 -0.1807

dydx = 5×1

1.0e-13 * 0.1490 0 NaN 0 -0.0000

dydx = 5×1

1.0e-13 * 0 -0.1490 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-13 * 0 0 NaN 0.1490 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-33 * 0 NaN NaN 0 -0.1807

dydx = 5×1

1.0e-13 * -0.1490 NaN NaN 0 -0.0000

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-13 * 0 NaN NaN 0.1490 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-33 * 0 0 NaN 0 -0.1807

dydx = 5×1

1.0e-13 * 0.1490 0 NaN 0 -0.0000

dydx = 5×1

1.0e-13 * 0 -0.1490 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-13 * 0 0 NaN 0.1490 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-33 * 0 NaN NaN 0 -0.1807

dydx = 5×1

1.0e-13 * -0.1490 NaN NaN 0 -0.0000

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-13 * 0 NaN NaN 0.1490 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-33 * 0 0 NaN 0 -0.1807

dydx = 5×1

1.0e-13 * 0.1490 0 NaN 0 -0.0000

dydx = 5×1

1.0e-13 * 0 -0.1490 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-13 * 0 0 NaN 0.1490 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-33 * 0 NaN NaN 0 -0.1807

dydx = 5×1

1.0e-13 * -0.1490 NaN NaN 0 -0.0000

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-13 * 0 NaN NaN 0.1490 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-33 * 0 0 NaN 0 -0.1807

dydx = 5×1

1.0e-13 * 0.1490 0 NaN 0 -0.0000

dydx = 5×1

1.0e-13 * 0 -0.1490 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-13 * 0 0 NaN 0.1490 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-33 * 0 NaN NaN 0 -0.1807

dydx = 5×1

1.0e-13 * -0.1490 NaN NaN 0 -0.0000

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-13 * 0 NaN NaN 0.1490 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-33 * 0 0 NaN 0 -0.1807

dydx = 5×1

1.0e-13 * 0.1490 0 NaN 0 -0.0000

dydx = 5×1

1.0e-13 * 0 -0.1490 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-13 * 0 0 NaN 0.1490 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-33 * 0 NaN NaN 0 -0.1807

dydx = 5×1

1.0e-13 * -0.1490 NaN NaN 0 -0.0000

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-13 * 0 NaN NaN 0.1490 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-33 * 0 0 NaN 0 -0.1807

dydx = 5×1

1.0e-13 * 0.1490 0 NaN 0 -0.0000

dydx = 5×1

1.0e-13 * 0 -0.1490 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-13 * 0 0 NaN 0.1490 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-33 * 0 NaN NaN 0 -0.1807

dydx = 5×1

1.0e-13 * -0.1490 NaN NaN 0 -0.0000

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-13 * 0 NaN NaN 0.1490 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-33 * 0 0 NaN 0 -0.1807

dydx = 5×1

1.0e-13 * 0.1490 0 NaN 0 -0.0000

dydx = 5×1

1.0e-13 * 0 -0.1490 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-13 * 0 0 NaN 0.1490 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-33 * 0 NaN NaN 0 -0.1807

dydx = 5×1

1.0e-13 * -0.1490 NaN NaN 0 -0.0000

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-13 * 0 NaN NaN 0.1490 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-33 * 0 0 NaN 0 -0.1807

dydx = 5×1

1.0e-13 * 0.1490 0 NaN 0 -0.0000

dydx = 5×1

1.0e-13 * 0 -0.1490 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-13 * 0 0 NaN 0.1490 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-33 * 0 NaN NaN 0 -0.1807

dydx = 5×1

1.0e-13 * -0.1490 NaN NaN 0 -0.0000

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-13 * 0 NaN NaN 0.1490 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-33 * 0 0 NaN 0 -0.1807

dydx = 5×1

1.0e-13 * 0.1490 0 NaN 0 -0.0000

dydx = 5×1

1.0e-13 * 0 -0.1490 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-13 * 0 0 NaN 0.1490 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-33 * 0 NaN NaN 0 -0.1807

dydx = 5×1

1.0e-13 * -0.1490 NaN NaN 0 -0.0000

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-13 * 0 NaN NaN 0.1490 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-33 * 0 0 NaN 0 -0.1807

dydx = 5×1

1.0e-13 * 0.1490 0 NaN 0 -0.0000

dydx = 5×1

1.0e-13 * 0 -0.1490 NaN 0 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-13 * 0 0 NaN 0.1490 0

dydx = 5×1

0 0 NaN 0 0

dydx = 5×1

1.0e-33 * 0 NaN NaN 0 -0.1807

dydx = 5×1

1.0e-13 * -0.1490 NaN NaN 0 -0.0000

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

1.0e-13 * 0 NaN NaN 0.1490 0

dydx = 5×1

0 NaN NaN 0 0

dydx = 5×1

0 NaN NaN 0 0

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

Error in solution>william (line 42)
sol1 = bvp4c(@williamode,@williambc,solinit,options,w,Ha,Re,angle_degrees,E,Pr,phi1,phi2,rof,ro1,ro2,rocpf,rocp1,rocp2,kf,k1,k2,sigmaf,sigma1,sigma2);

function william

clc

clear all format long

w=1; %wlmsn

Ha=0.1;

Re=0.4;

angle_degrees=0.1; %omega N,a,Ha,Re,angle_degrees,E,Pr

E=0.1; %Ec

Pr=0.2; %0.01

phi1=0.001;%0.02,0.03

phi2=0.001;%0.03,0.2

rof=997.1;

ro1=8933;

ro2=3970;

rocpf=4179;

rocp1= 385;

rocp2= 765;

kf=0.613;

k1=401;

k2=40

sigmaf=0.05;

sigma1=5.96*10^7;

sigma2=3.69*10^7;

A1=(phi2*rocp2)/rocpf+ (1-phi2)*((1-phi1)+(rocp1*phi1)/rocpf);

A2=((1-phi2)*((1-phi1)+(ro1*phi1)/rof)+(ro2*phi2)/rof);

A= ((sigma1*(1-2*(phi1)) + 2*sigmaf*(1-phi1))/(sigma1*(1-phi1) + 2*sigmaf*(1+phi1))); %sigmaf

A3=((sigma2*(1+2*(phi2))+2*(1-phi2)*A)/(sigma2*(1-phi2)+(2+phi2)*A))*A;

%A3=((sigma2+2*(1-phi2)*(sigma1 + 2*sigmaf - 2*phi1*(sigmaf - sigma1)) * sigmaf / (sigma1 + 2*sigmaf + phi1 * (sigmaf - sigma1))+2*phi2*sigma2)*(sigma1 + 2*sigmaf - 2*phi1*(sigmaf - sigma1)) * sigmaf / (sigma1 + 2*sigmaf + phi1 * (sigmaf - sigma1)))/(sigma2+2*(1+phi2)*(sigma1 + 2*sigmaf - 2*phi1*(sigmaf - sigma1)) * sigmaf / (sigma1 + 2*sigmaf + phi1 * (sigmaf - sigma1))-phi2*sigma2);

A4=((1-phi1)^-2.5)*((1-phi2)^-2.5); %meuf

A5=(((2 * (1 + phi1) * (2 * kf - 2 * phi2 * (k2 - kf) + k2)) / (2 * kf + phi2 * (k2 - kf) + k2) + ((1 - 2 * phi1) * k1) / kf) / (2 - phi1)) * ((2 * kf - 2 * phi2 * (k2 - kf) + k2) / (2 * kf + phi2 * (k2 - kf) + k2)) + ((1 + phi1) * k1) / kf;

infinity=1;

solinit = bvpinit(linspace(0,infinity,20),zeros(5,1));

options=bvpset('Stats','on','RelTol',1e-6);

lines={'k','r','g','m','k--','r--','g--','b--','y','m','k','b'};

Ha=0.1;

sol1 = bvp4c(@williamode,@williambc,solinit,options,w,Ha,Re,angle_degrees,E,Pr,phi1,phi2,rof,ro1,ro2,rocpf,rocp1,rocp2,kf,k1,k2,sigmaf,sigma1,sigma2);

Ha=0.3;

sol2 =bvp4c(@williamode,@williambc,solinit,options,w,Ha,Re,angle_degrees,E,Pr,phi1,phi2,rof,ro1,ro2,rocpf,rocp1,rocp2,kf,k1,k2,sigmaf,sigma1,sigma2);

Ha=0.5;

sol3 =bvp4c(@williamode,@williambc,solinit,options,w,Ha,Re,angle_degrees,E,Pr,phi1,phi2,rof,ro1,ro2,rocpf,rocp1,rocp2,kf,k1,k2,sigmaf,sigma1,sigma2);

Ha=0.7;

sol4= bvp4c(@williamode,@williambc,solinit,options,w,Ha,Re,angle_degrees,E,Pr,phi1,phi2,rof,ro1,ro2,rocpf,rocp1,rocp2,kf,k1,k2,sigmaf,sigma1,sigma2);

figure(1);

plot(sol1.x,sol1.y(1,:),lines{1},sol2.x,sol2.y(1,:),lines{2},sol3.x,sol3.y(1,:),lines{3},sol4.x,sol4.y(1,:),lines{4},'LineWidth',3,'MarkerSize',16,'linestyle','-');

xlabel('\zeta','Interpreter','tex','FontSize',16,'FontWeight','bold');

ylabel('\eta','Interpreter','tex','FontSize',16,'FontWeight','bold');

grid on

hold on

figure(2);

plot(sol1.x,sol1.y(4,:),lines{1},sol2.x,sol2.y(4,:),lines{2},sol3.x,sol3.y(4,:),lines{3},sol4.x,sol4.y(4,:),lines{4},'LineWidth',3,'MarkerSize',16,'linestyle','-');

xlabel('\zeta','Interpreter','tex','FontSize',16,'FontWeight','bold');

ylabel('\kappa','Interpreter','tex','FontSize',16,'FontWeight','bold');

grid on

hold on

y1 = sol1.y;

y2 = sol2.y;

function dydx = williamode(x,y,w,Ha,Re,angle_degrees,E,Pr,phi1,phi2,rof,ro1,ro2,rocpf,rocp1,rocp2,kf,k1,k2,sigmaf,sigma1,sigma2)

dydx =zeros(5,1);

dydx = [y(2)

y(3)

%-(sqrt((2*y(1)*angle_degrees)^2 + y(2)^2) / (sqrt((2*y(1)*angle_degrees)^2 + y(2)^2) + w * (2 * y(2)^2 + 4 * y(1)^2 * angle_degrees^2))) * (2 * angle_degrees * Re * A2 * (1 - phi1)^2.5 * (1 - phi2)^2.5 * y(1) * y(2)+(4-A3*(1-phi1)^2.5*(1-phi2)^2.5*(Ha)^2)*y(2)*angle_degrees^2+(w*(sqrt(2*y(1)*angle_degrees)^2+y(2)^2)*((16*y(1)^3*angle_degrees^4*+8*y(1)*y(2)^2*angle_degrees^2+2*y(2)^2*y(3)+4*y(1)^2*y(3)*angle_degrees^2)/(4*y(1)*y(2)*angle_degrees^2+y(2)*y(3))+(1/((2*y(1)*angle_degrees)^2*+y(2)^2))*(80*y(1)^2*y(2)*angle_degrees^4+32*y(1)*y(2)*y(3)*angle_degrees^2+8*y(2)^3*angle_degrees^2+4*y(2)*y(3)^2)));

-(sqrt((2*y(1)*angle_degrees)^2+y(2)^2)/((sqrt((2*y(1)*angle_degrees)^2+y(2)^2))+w*(2*y(2)^2+4*y(1)^2*angle_degrees^2)))*(2*angle_degrees*Re*A2*(1-phi1)^2.5*(1-phi2)^2.5*y(1)*y(2)+(4-A3*(1-phi1)^2.5*(1-phi2)^2.5*(Ha)^2)*y(2)*angle_degrees^2+((w*(sqrt(2*y(1)*angle_degrees)^2+y(2)^2))*((16*y(1)^3*angle_degrees^4*+8*y(1)*y(2)^2*angle_degrees^2+2*y(2)^2*y(3)+4*y(1)^2*y(3)*angle_degrees^2)/(4*y(1)*y(2)*angle_degrees^2+y(2)*y(3)))+((1/((2*y(1)*angle_degrees)^2*+y(2)^2))*(80*y(1)^2*y(2)*angle_degrees^4+32*y(1)*y(2)*y(3)*angle_degrees^2+8*y(2)^3*angle_degrees^2+4*y(2)*y(3)^2))))

%-(sqrt((2 * y(1) * angle_degrees)^2 + y(2)^2) /(sqrt((2 * y(1) * angle_degrees)^2 + y(2)^2) + w * (2 * y(2)^2 + 4 * y(1)^2 * angle_degrees^2)))*(2*angle_degrees *Re*A2*(1 - phi1)^2.5*(1 - phi2)^2.5 * y(1) * y(2) +(4 - A3 * (1 - phi1)^2.5 * (1 - phi2)^2.5 * (Ha)^2) * y(2) * angle_degrees^2 +((w * (sqrt(2 * y(1) * angle_degrees)^2 + y(2)^2)) *((16 * y(1)^3 * angle_degrees^4 + 8 * y(1) * y(2)^2 * angle_degrees^2 + 2 * y(2)^2 * y(3) +4 * y(1)^2 * y(3) * angle_degrees^2) /(4 * y(1) * y(2) * angle_degrees^2 + y(2) * y(3)) +((1 / ((2 * y(1) * angle_degrees)^2 + y(2)^2)) *(80 * y(1)^2 * y(2) * angle_degrees^4 + 32 * y(1) * y(2) * y(3) * angle_degrees^2+8 * y(2)^3 * angle_degrees^2 + 4 * y(2) * y(3)^2)));

y(5)

(-1/A5)*((E*Pr*A1)/(1-phi1)^2.5*(1-phi2)^2.5)*((4*y(1)^2*angle_degrees^2+y(2)^2)+w*((4*y(1)^2*angle_degrees^2+y(2)^2)^3/2))]

end

function res = williambc(ya,yb,w,Ha,Re,angle_degrees,E,Pr,phi1,phi2,~,ro1,ro2,rocpf,rocp1,rocp2,kf,k1,k2,sigmaf,sigma1,sigma2)

res =[ya(1)-1;

ya(2);

ya(5);

yb(1);

yb(4)-1;];

hold on

end

grid on

end

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Torsten on 12 Nov 2024

As long as you get NaN values inside the dydx-vector, bvp4c won't succeed.

A starting point for changes in your code is to observe that you divide by y(1) to compute dydx(3), but that the initial value for y(1) is set to 0.

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Answer 1

Sandeep Mishra on 25 Nov 2024 at 11:55

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https://nl.mathworks.com/matlabcentral/answers/2165719-how-can-i-remove-singular-jacobin-error-from-this-code#answer_1549463

Open in MATLAB Online

Hi Sharqa,

I encountered a similar error when running the provided code snippet in MATLAB R2024b.

I found a relevant MATLAB Answers post addressing the similar issue: https://www.mathworks.com/matlabcentral/answers/120468-why-do-i-receive-an-error-about-a-singular-jacobian-when-i-use-the-bvp4c-function-within-matlab#answer_127315

In the given code snippet, a 5x1 zero vector is being passed as the initial guess for the solution, which is leading to the occurrence of 'NaN' values in the 'dydx' variable.

To resolve the issue, you can modify the initial guess for the solution to more appropriate values.

Refer to the following example code snippet to initialize the initial guess values:

solinit = bvpinit(linspace(0,infinity,20),[12; 10; 1; 7; 4]);

Refer to the following MathWorks Documentation to learn more about ‘bvp4c’ function:

https://www.mathworks.com/help/releases/R2024b/matlab/ref/bvp4c.html

I hope this helps!

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How can i remove singular Jacobin error from this code?

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How can i remove singular Jacobin error from this code?

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