Bvp4c Unable to solve the collocation equations -- a singular Jacobian Encountered
3 views (last 30 days)
Show older comments
I have a coupled non-linear differential equations u''-b1*(t')*(u')+(1+b1*t)*[G1*F1*t+G2*F1*p-F3*P]=0; t''-b2*(t')^2+B*F6*(u')^2+(b2-b1)*t*B*F6*(u')^2-b2*b1*B*F6*t^2*(u')^2=0; p''- A*p=0 and the boundary conditions are u=0,t=1+m,p=1+n at y=-1 and u=0,t=0,p=1 at y=1.
The code is:
clc;
p=0.01;
Betaf= 207;
Betas = 17;
Beta = 0.5;
kof = 0.613;
kos = 400;
m = 1;
b2 = 0.5;
b1 = 0.5;
G1 = 5;
G2 = 5;
A = 0.5;
Rhof = 997.1;
Rhos = 8933;
P = 0.5;
n=0.3;
B=0.01;
A1 = (1-p).^2.5;
A2 = 1/(1 + 1/Beta);
A3 = (1-p)+p.*((Rhos.*Betas)./(Rhof.*Betaf));
F1 = A2.*A3;
F3 = A1.*A2;
F4 = (kos + 2*kof - 2*p.*(kof - kos))/(kos + 2*kof + p.*(kof - kos));
F5 = (1 + 1/Beta)./A1;
F6 = F5./F4;
dydx=@(x,y)[y(2);
y(4);
y(5);
(b1.*y(4).*y(2)-(1+b1.*y(3)).*(G1.*F1.*y(3)+G2.*F1.*y(5)-F3.*P));
b2.*y(4).^2-B.*F6.*y(2).^2+(bk-bv).*y(3).*B.*F6.*y(2).^2-b2.*b1.*B.*F6.*y(3).^2*y(2).^2;
Alpha.*y(5)];
BC=@(ya,yb)[ya(1);yb(1);ya(3)-(1+m);yb(3)-1;ya(5)-(1+n);yb(5)];
yint=@(x)[0.01;0.01;0.01;0.01;0.01;0.01];
solint=bvpinit(linspace(-1,1,50),yint);
S=bvp4c(dydx,BC,solint)
for i=1:6
S=bvp4c(dydx,BC,S);
end
The error I get is “Unable to solve the collocation equations -- a singular Jacobian Encountered”.
I tried using different guess in the statement yint=@(x)[0.01;0.01;0.01;0.01;0.01;0.01];
But still the error persist.
Please help me with my code.
0 Comments
Accepted Answer
Torsten
on 7 Oct 2022
Edited: Torsten
on 7 Oct 2022
clc;
p = 0.01;
Betaf = 207;
Betas = 17;
Beta = 0.5;
kof = 0.613;
kos = 400;
m = 1;
b2 = 0.5;
b1 = 0.5;
G1 = 5;
G2 = 5;
A = 0.5;
Rhof = 997.1;
Rhos = 8933;
P = 0.5;
n = 0.3;
B = 0.01;
A1 = (1-p).^2.5;
A2 = 1/(1 + 1/Beta);
A3 = (1-p)+p.*((Rhos.*Betas)./(Rhof.*Betaf));
F1 = A2.*A3;
F3 = A1.*A2;
F4 = (kos + 2*kof - 2*p.*(kof - kos))/(kos + 2*kof + p.*(kof - kos));
F5 = (1 + 1/Beta)./A1;
F6 = F5./F4;
dydx=@(x,y)[y(4);
y(5);
y(6);
b1.*y(4).*y(5)-(1+b1.*y(2)).*(G1.*F1.*y(2)+G2.*F1.*y(3)-F3.*P);
b2.*y(5).^2-B.*F6.*y(4).^2-(b2-b1).*y(2).*B.*F6.*y(4).^2+b2.*b1.*B.*F6.*y(2).^2*y(4).^2;
A.*y(3)];
BC = @(ya,yb)[ya(1);yb(1);ya(2)-(1+m);yb(2);ya(3)-(1+n);yb(3)-1.0];
yinit = [0.01;0.01;0.01;0.01;0.01;0.01];
solint = bvpinit(linspace(-1,1,50),yinit);
S = bvp4c(dydx,BC,solint);
plot(S.x,[S.y(1,:);S.y(2,:);S.y(3,:)])
More Answers (0)
See Also
Categories
Find more on Partial Differential Equation Toolbox in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!