I am trying to solve a system of ordinary differential equations using Bvp4c but I get a message error that a singular Jacobian encountered, below the code I am working on
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test3()
function test3
clear
clc
close all
format long
%% ------------------------------------------------------------------------
% Parameters
%--------------------------------------------------------------------------
NP=100; %the number of meshpoints
eta_infty =15;
%% ------------------------------------------------------------------------
for i=1:5
A=[2 3 4 5 6];
gamma=A(i);
eps=0.001; %A=0.1*[2 4 6 8 9]; %Medium porosity
Beta=0.5; %A=0.1*[1 2 3 4 5]; %Beta casson parameter
Omega=7; %A=[4 5 6 7 8]; %cylinder curvature parameter
M=6; %A=[2 3 4 5 6]; %magnetic field parameter
P=5; %A=[3 4 5 6 7]; %porous medium parameter
Gr=0.2; %A=[0 2 3 4 5]; %themal Grashof number
Gm=0.3; %mass Grashof number
Alpha=20; %curvature angel
Pr=7.56; %for water7.56 %prentdl number
Rd=0; %A=0.1*[0 1 3 5 7]; %Radiation parameter
Ec=0.01; %Eckert number
Nt=0.3; %A=0.1*[1 2 3 4 5]; %thermophoresis parameter
Nb=0.2; %A=0.1*[2 3 4 5 6]; %Brownian motion parameter
Sc=5; %A=[5 7 9 11 13]; %Schmidt number
%gamma=3; %A=[2 3 4 5 6];
xi_1=0.001;
xi_2=0.001;
QM=0.01; %mass flux
QH=0.01; %heat flux
%--------------------------------------------------------------------------
%lamda=0.001; %A=[0.001 0.002 0.003 0.004 0.005];lamda parameter
%Pe=Re*Pr; % peclet number
%Re=0.001;
%A1=1/Pr;
%A2=1/Sc;
%--------------------------------------------------------------------------
% Solve the problem
%--------------------------------------------------------------------------
int=ones(1,7); %We have 7 variables
int=0.*int;
% int=[0 0 -0.003 -0.35 0 0 -0.05];
options = [];
solinit = bvpinit(linspace(0,eta_infty,NP),int);
sol = bvp4c(@fsode,@fsbc,solinit,options);
eta = sol.x; %this is eta
f = sol.y; %These are the dependenat variables
FF=f(1,:);
DF=f(2,:);
%DDF(i)=-f(3,1)
TH=f(4,:);
%DTH(i)=f(5,1);
Fi =f(6,:);
%QH=(1+xi_2)*gamma+(1/Pr)*(1+((4*Rd)/3))*DTH;
%% ------------------------------------------------------------------------
% Plot the results
% The model equations
%--------------------------------------------------------------------------
end
function dfdeta = fsode(eta,Y)
F(1) = Y(2);
F(2) = Y(3);
F(3) =(-eps*((1+(1/Beta))*(1+(2*Omega*eta))))*(((2*Omega*(1+(1/Beta))*Y(3))/eps)+(1/eps^2)*(Y(1)*Y(3)-(Y(2))^2)-(M+P)*Y(2)+(Gr*Y(4)-Gm*Y(6))*cosd(Alpha));
F(4)=Y(5);
F(5)=(-Pr/((1+(2*Omega*eta))*(1+((4/3)*Rd))))*(((2*Omega*(1+((4/3)*Rd))*Y(5))/Pr)+((1+(1/Beta))*(1+(2*Omega*eta))*Ec*(Y(3))^2)+((1+(2*Omega*eta))*((Nt*(Y(5))^2)-(Nb*Y(5)*Y(7))))+(M*Ec*(Y(2))^2)+(Y(1)*Y(5)));
F(6)=Y(7);
F(7)=(-1/(1+(2*Omega*eta)))*((2*Omega*Y(7))-((Nt/Nb)*(((1+(2*Omega*eta))*F(5))+(2*Omega*Y(5))))+(Sc*Y(1)*Y(7)));
dfdeta = [ F(1)
F(2)
F(3)
F(4)
F(5)
F(6)
F(7)
];
end
% --------------------------------------------------------------------------
function res = fsbc(ya,yb)
res = [ya(1)-gamma % f-gamma=0
ya(2) % f'=0
ya(4)-1 %TH=1
((Sc/eps)*(ya(6)-xi_1)*ya(1))+ya(7)+((Nt/Nb)*ya(5))-QM %Mass flux
yb(2) %f'=0
yb(7)-1 %phi=1
(((1+(2*Omega*eta_infty))^(-1/2))*(yb(4)+xi_2)*yb(1))+((1/Pr)*((1+(2*Omega*eta_infty))^(-1/2))*(1+((4/3)*Rd))*yb(5))-QH %Heat flux
];
end
end
2 Commenti
Torsten
il 17 Gen 2024
This error message usually appears if there is something wrong in the setup of your model equations and/or boundary conditions. So we cannot help in this case apart from saying: Recheck your model equations and boundary conditions and their implementation in the code.
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