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

Question

Ben Miller 2020-4-4

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/515379-error-using-bvp4c-line-251-unable-to-solve-the-collocation-equations-a-singular-jacobian-encoun

编辑： Torsten 2022-10-30

采纳的回答： Harshendra Shah

在 MATLAB Online 中打开

Hello

I'm trying to solve an ODE, but getting the following error:

Error using bvp4c (line 251)

Unable to solve the collocation equations -- a singular Jacobian encountered.

Here is my code:

Diff=7.0000e-11;
koffPart=5.1910e-06;
konPart=6.7702e-18;
CT=1.2044e+17;
LT=1.2044e+16;
xmesh = linspace(0,1000,100);
solinit = bvpinit(xmesh, @guess);
sol = bvp4c(@(t,C) odefcn(t,C,Diff,konPart,koffPart,CT,LT), @(Ca,Cb) bcfcn(Ca,Cb,CT), solinit);

Here is my ODE function:

function dCdt = odefcn(t,C,Diff,konPart,koffPart,CT,LT)
    dCdt=zeros(2,1);
    dCdt(1)=C(2);
    dCdt(2)=(C(2)+konPart*C(1)*(LT-CT+C(1))-koffPart*(CT-C(1)))/Diff;
end

Here are my boundary conditions:

function res = bcfcn(Ca,Cb,CT)
res = [Ca(1)-CT
       Cb(2)];
end

And my guess:

function g = guess(x)
g = [exp(-x)
     -exp(-x)];
end

I'd really appreiate any help.

Thanks!

Ben

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Muhammad Safdar Nadeem 2022-10-30

function newpapercode

m=0;

zeta=0.5;

xi=1;

rho_s=997;

rho_f=4179;

M=30;

C_T=0;

P_rf=0.1;

E_c=0.5;

P_rf=1;

K_f=1;

K_fn=.1;

n=0.006;

eta=0.5;

lamda=1;

rho_cps=993;

rho_cpf=0.001;

gamma=1;

omega=1;

F_n=1;

lambda_u=2;

K_f=0;

K_fn=1;

N=1;

S=1;

sol = bvpinit(linspace(0,4,100),[0 0 0 0 0 ]);

sol1 = bvp4c(@bvpexam2, @bcexam2, sol);

x1 = sol1.x;

y1 = sol1.y;

figure (1)

plot(x1, y1(2,:));

hold on

% figure (2)

% plot(x1, y1(4,:));

% hold on

% figure (3)

% plot(x1, y1(6,:));

% hold on

% figure (4)

% plot(x1, y1(8,:));

% hold on

z = y1(3,1);

p = y1(7,1);

function res = bcexam2(y0, yinf)

res=[y0(1)+2*S/m+1;y0(2)-0;y0(4)-1;yinf(2)-1;yinf(4)-0];

end

function ysol = bvpexam2(~,y)

yy1 = ((2/m+1)*(1-zeta)^2.5*(xi)*(xi)/(1-zeta+zeta*(rho_s/rho_f)))*((M+lamda/(1-zeta)^2.5)*(y(2)-1)+(xi/1-m)*(1-zeta+zeta*(rho_cps/rho_cpf))*(gamma)*(sin(omega/2)))+(1-zeta+zeta*(rho_s/rho_f))*(1-zeta)^2.5*(((2)*(m-F_n)*(y(2)*y(2)-1))/(m+1)+y(1)*y(3)-lambda_u*(2-eta*y(3)-2*y(2)));

yy2 = (-4/3)*(K_f/K_fn)*(N)*((C_T+y(4))^3*y(5))-((P_rf)*(E_c)*y(3)*y(3))/(1-zeta)^2.5+(P_rf)*(1-zeta+zeta*(rho_cps/rho_cpf))*(K_f/K_fn)*(((2)*(n)*(y(2))*(y(4)))/(m+1)-(y(1)*y(5))+(lambda_u*eta*y(5)));

ysol = [y(2);y(3);yy1;y(5);yy2;];

end

Muhammad Safdar Nadeem 2022-10-30

please help me in this error

Error using bvp4c (line 251)

Unable to solve the collocation equations -- a singular Jacobian encountered.

Error in newpapercodeH (line 28)

sol1 = bvp4c(@bvpexam2, @bcexam2, sol);

Torsten 2022-10-30

编辑：Torsten 2022-10-30

在 MATLAB Online 中打开

You use

res=[y0(1)+2*S/m+1;y0(2)-0;y0(4)-1;yinf(2)-1;yinf(4)-0];

in your code, but m = 0. So S/m means that you divide by 0.

Maybe you meant S/(m+1) instead of S/m+1.

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Answer 1

Harshendra Shah 2020-4-7

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/515379-error-using-bvp4c-line-251-unable-to-solve-the-collocation-equations-a-singular-jacobian-encoun#answer_424500

Hi Ben,

A singular Jacobian indicates that the initial guess causes the solution to diverge. The BVP4C function finds the solution by solving a system of nonlinear algebraic equations. Nonlinear solvers are only as effective as the initial guess they start with, so changing your starting guess may help. Also, BVP4C is responsible for providing a guess for the solution from one iteration to another.

This issue can occur due to multiple reasons. You can find the same in this MATLAB Answers page: 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

This MATLAB Answer also suggests some workarounds to solve this issue.

I hope this helps.