what is the error here?

here is the code .

slipflow()

Unrecognized function or variable 'S'.

Error in solution>OdeBVP (line 110)
f =[y(2);y(3);(1/3)*D1*((y(2)^2)-2*(y(1)*y(3))+2*S);y(5);-2/3*(Pr*((H4/H3)/kh)*y(1)*y(5))];

Error in solution>@(x,y)OdeBVP(x,y,Pr,D1,Kh,H4,H3) (line 57)
sol = bvp4c (@(x,y)OdeBVP(x,y,Pr,D1,Kh,H4,H3), @(ya,yb)OdeBC(ya, yb, A, S, lambda), solinit, options);

Error in bvparguments (line 96)
testODE = ode(x1,y1,odeExtras{:});

Error in bvp4c (line 119)
bvparguments(solver_name,ode,bc,solinit,options,varargin);

Error in solution>slipflow (line 57)
sol = bvp4c (@(x,y)OdeBVP(x,y,Pr,D1,Kh,H4,H3), @(ya,yb)OdeBC(ya, yb, A, S, lambda), solinit, options);

function slipflow
format long g
%Define all parameters
% Boundary layer thickness & stepsize
etaMin = 0;
etaMax1 = 15;
etaMax2 = 15; %15, 10
stepsize1 = etaMax1;
stepsize2 = etaMax2;
% Input for the parameters
A=1;  %velocity slip
B=0.2;  %thermal slip
beta=0.02;  %heat gen/abs
S=2.4;  %suction(2.3,2.4,2.5)
Pr=6.2;     %prandtl number
lambda=-1;  %stretching shrinking
a=0.01; %phil-1st nanoparticle concentration
b=0.01; %(0.01,0.05)phi2-2nd nanoparticle concentration
c=a+b;  %phi-hnf concentration of hybrid nanoparticle 
%%%%%%%%%%% 1st nanoparticle properties (Al2O3)%%%%%%%%%%%%
C1=765;
P1=3970;
K1=40;
B1=0.85/((10)^5);
s1=35*(10)^6; %MHD
%%%%%%%%%%% 2nd nanoparticle properties (Cu)%%%%%%%%%%%%
C2=385; %specific heat
P2=8933; %density
K2=400; %thermal conductivity
B2=1.67/((10)^5);   %thermal expansion
s2=(59.6)*(10)^6; %MHD
%%%%%%%%%%% Base fluid properties %%%%%%%%%%%%
C3=4179; %specific heat
P3=997.1; %density
K3=0.613; %thermal conductivity
B3=21/((10)^5);   %thermal expansion
s3=0.05; %MHD
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%multiplier%%%%%%%%%%%%%%%%%%%
H1=P1*C1;       %pho*cp nanoparticle 1
H2=P2*C2;       %pho*cp nanoparticle 2
H3=P3*C3;       %pho*cp base fluid
H4=a*H1+b*H2+(1-c)*H3; %pho*cp hybrid nanofluid
H5=a*P1+b*P2+(1-c)*P3;  %pho hybrid nanofluid
H6=1/((1-c)^2.5);   % mu hybrid nanofluid / mu base fluid
H7=a*(P1*B1)+b*(P2*B2)+(1-c)*(P3*B3);   % thermal expansion of hybrid nanofluid
%Kn=K3*(K1+2*K3-2*a*(K3-K1))/(K1+2*K3+a*(K3-K1));     %thermal conductivity of nanofluid
Kh=(((a*K1+b*K2)/c)+2*K3+2*(a*K1+b*K2)-2*c*K3)/(((a*K1+b*K2)/c)+2*K3-(a*K1+b*K2)-2*c*K3); %khnf/kf
H8=(((a*s1+b*s2)/c)+2*s3+2*(a*s1+b*s2)-2*c*s3)/(((a*s1+b*s2)/c)+2*s3-(a*s1+b*s2)-2*c*s3); % \sigma hnf/ \sigma f
D1=(H5/P3)/H6;
D3=(H7/(P3*B3))/(H5/P3);                % multiplier of boundary parameter
D2= Pr*((H4/H3)/Kh);
D4=H8/(H5/P3);  %multiplier MHD
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% First solution %%%%%%%%%%%%%%%%%%%
options = bvpset('stats','off','RelTol',1e-10);
solinit = bvpinit (linspace (etaMin, etaMax1, stepsize1),@(x)OdeInit1(x,A,S,lambda));
sol = bvp4c (@(x,y)OdeBVP(x,y,Pr,D1,Kh,H4,H3), @(ya,yb)OdeBC(ya, yb, A, S, lambda), solinit, options);
eta = linspace (etaMin, etaMax1, stepsize1);
y= deval (sol,eta);
figure(1)   %velocity profile
plot(sol.x,sol.y(2,:),'-')
xlabel('\eta')
ylabel('f`(\eta)')
hold on
figure(2)   %temperature profile
plot(sol.x,sol.y(4,:),'-')
xlabel('\eta')
ylabel('\theta(\eta)')
hold on
% saving the out put in text file for first solution
descris =[sol.x; sol.y];
save 'sliphybrid_upper.txt' descris -ascii
% Displaying the output for first solution
fprintf('\n First solution:\n');
fprintf('f"(0)=%7.9f\n',y(3));  % reduced skin friction 
fprintf('-theta(0)=%7.9f\n',-y(5)); %reduced local nusselt number
fprintf('Cfx=%7.9f\n',H6*(y(3)));    %  skin friction 
fprintf('Nux=%7.9f\n',-Kh*y(5));     % local nusselt number
fprintf('\n');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% second solution %%%%%%%%%%%%%%%%%%%
options = bvpset('stats','off','RelTol',1e-10);
solinit = bvpinit (linspace (etaMin, etaMax2, stepsize2),@(x)OdeInit2(x,A,S,lambda));
sol = bvp4c (@(x,y)OdeBVP(x,y,Pr,D1,Kh,H4,H3), @(ya,yb)OdeBC(ya, yb, A, S, lambda), solinit, options);
eta= linspace (etaMin, etaMax2, stepsize2);
y = deval (sol,eta);
figure(1)   %velocity profile
plot(sol.x,sol.y(2,:),'--')
xlabel('\eta')
ylabel('f`(\eta)')
hold on
figure(2)   %temperature profile
plot(sol.x,sol.y(4,:),'--')
xlabel('\eta')
ylabel('\theta(\eta)')
hold on
% saving the out put in text file for second solution
descris=[sol.x; sol.y];
save 'sliphybrid_lower.txt'descris -ascii
% Displaying the output for first solution
fprintf('\nSecond solution:\n');
fprintf('f"(0)=%7.9f\n',y(3));  % reduced skin friction 
fprintf('-theta(0)=%7.9f\n',-y(5)); %reduced local nusselt number
fprintf('Cfx=%7.9f\n',H6*(y(3)));    %  skin friction 
fprintf('Nux=%7.9f\n',-Kh*y(5));     % local nusselt number
fprintf('\n');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
end
% Define the ODE function
function f = OdeBVP(x,y,Pr,D1,Kh,H4,H3)
f =[y(2);y(3);(1/3)*D1*((y(2)^2)-2*(y(1)*y(3))+2*S);y(5);-2/3*(Pr*((H4/H3)/kh)*y(1)*y(5))];
end
% Define the boundary conditions
function res = OdeBC(ya, yb, A, S, lambda)
res= [ya(1)-S;ya(2)-lambda;ya(4)-1;yb(3)-1;yb(4)];
end
% setting the initial guess for first solution
function v = OdeInit1(x,A,S,lambda)
v=[S+0.56;0;0;0;0];
end
% setting the initial guess for second solution
function v1 =OdeInit2(x, A, S,lambda)
v1 = [exp(-x);exp(-x);-exp(-x);-exp(-x);-exp(-x)];
end

Answer 1

[Torsten]

The error is that the parameter "S" is not an input to function "odeBVP" and thus undefined in

f =[y(2);y(3);(1/3)*D1*((y(2)^2)-2*(y(1)*y(3))+2*S);y(5);-2/3*(Pr*((H4/H3)/kh)*y(1)*y(5))];

[Yasir]

This is not working

[Torsten]

It's technically working now (see below), but the solver has problems with your equations.

Where did you find the original working code ? What changes did you make that it doesn't work any longer ?

Maybe you could include the mathematical form of your problem so that we could compare with your code.

slipflow()

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

Error in solution>slipflow (line 57)
sol = bvp4c (@(x,y)OdeBVP(x,y,Pr,D1,Kh,H4,H3,S), @(ya,yb)OdeBC(ya, yb, A, S, lambda), solinit, options);

function slipflow
format long g
%Define all parameters
% Boundary layer thickness & stepsize
etaMin = 0;
etaMax1 = 15;
etaMax2 = 15; %15, 10
stepsize1 = etaMax1;
stepsize2 = etaMax2;
% Input for the parameters
A=1;  %velocity slip
B=0.2;  %thermal slip
beta=0.02;  %heat gen/abs
S=2.4;  %suction(2.3,2.4,2.5)
Pr=6.2;     %prandtl number
lambda=-1;  %stretching shrinking
a=0.01; %phil-1st nanoparticle concentration
b=0.01; %(0.01,0.05)phi2-2nd nanoparticle concentration
c=a+b;  %phi-hnf concentration of hybrid nanoparticle 
%%%%%%%%%%% 1st nanoparticle properties (Al2O3)%%%%%%%%%%%%
C1=765;
P1=3970;
K1=40;
B1=0.85/((10)^5);
s1=35*(10)^6; %MHD
%%%%%%%%%%% 2nd nanoparticle properties (Cu)%%%%%%%%%%%%
C2=385; %specific heat
P2=8933; %density
K2=400; %thermal conductivity
B2=1.67/((10)^5);   %thermal expansion
s2=(59.6)*(10)^6; %MHD
%%%%%%%%%%% Base fluid properties %%%%%%%%%%%%
C3=4179; %specific heat
P3=997.1; %density
K3=0.613; %thermal conductivity
B3=21/((10)^5);   %thermal expansion
s3=0.05; %MHD
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%multiplier%%%%%%%%%%%%%%%%%%%
H1=P1*C1;       %pho*cp nanoparticle 1
H2=P2*C2;       %pho*cp nanoparticle 2
H3=P3*C3;       %pho*cp base fluid
H4=a*H1+b*H2+(1-c)*H3; %pho*cp hybrid nanofluid
H5=a*P1+b*P2+(1-c)*P3;  %pho hybrid nanofluid
H6=1/((1-c)^2.5);   % mu hybrid nanofluid / mu base fluid
H7=a*(P1*B1)+b*(P2*B2)+(1-c)*(P3*B3);   % thermal expansion of hybrid nanofluid
%Kn=K3*(K1+2*K3-2*a*(K3-K1))/(K1+2*K3+a*(K3-K1));     %thermal conductivity of nanofluid
Kh=(((a*K1+b*K2)/c)+2*K3+2*(a*K1+b*K2)-2*c*K3)/(((a*K1+b*K2)/c)+2*K3-(a*K1+b*K2)-2*c*K3); %khnf/kf
H8=(((a*s1+b*s2)/c)+2*s3+2*(a*s1+b*s2)-2*c*s3)/(((a*s1+b*s2)/c)+2*s3-(a*s1+b*s2)-2*c*s3); % \sigma hnf/ \sigma f
D1=(H5/P3)/H6;
D3=(H7/(P3*B3))/(H5/P3);                % multiplier of boundary parameter
D2= Pr*((H4/H3)/Kh);
D4=H8/(H5/P3);  %multiplier MHD
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% First solution %%%%%%%%%%%%%%%%%%%
options = bvpset('stats','off','RelTol',1e-10);
solinit = bvpinit (linspace (etaMin, etaMax1, stepsize1),@(x)OdeInit1(x,A,S,lambda));
sol = bvp4c (@(x,y)OdeBVP(x,y,Pr,D1,Kh,H4,H3,S), @(ya,yb)OdeBC(ya, yb, A, S, lambda), solinit, options);
eta = linspace (etaMin, etaMax1, stepsize1);
y= deval (sol,eta);
figure(1)   %velocity profile
plot(sol.x,sol.y(2,:),'-')
xlabel('\eta')
ylabel('f`(\eta)')
hold on
figure(2)   %temperature profile
plot(sol.x,sol.y(4,:),'-')
xlabel('\eta')
ylabel('\theta(\eta)')
hold on
% saving the out put in text file for first solution
descris =[sol.x; sol.y];
save 'sliphybrid_upper.txt' descris -ascii
% Displaying the output for first solution
fprintf('\n First solution:\n');
fprintf('f"(0)=%7.9f\n',y(3));  % reduced skin friction 
fprintf('-theta(0)=%7.9f\n',-y(5)); %reduced local nusselt number
fprintf('Cfx=%7.9f\n',H6*(y(3)));    %  skin friction 
fprintf('Nux=%7.9f\n',-Kh*y(5));     % local nusselt number
fprintf('\n');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% second solution %%%%%%%%%%%%%%%%%%%
options = bvpset('stats','off','RelTol',1e-10);
solinit = bvpinit (linspace (etaMin, etaMax2, stepsize2),@(x)OdeInit2(x,A,S,lambda));
sol = bvp4c (@(x,y)OdeBVP(x,y,Pr,D1,Kh,H4,H3,S), @(ya,yb)OdeBC(ya, yb, A, S, lambda), solinit, options);
eta= linspace (etaMin, etaMax2, stepsize2);
y = deval (sol,eta);
figure(1)   %velocity profile
plot(sol.x,sol.y(2,:),'--')
xlabel('\eta')
ylabel('f`(\eta)')
hold on
figure(2)   %temperature profile
plot(sol.x,sol.y(4,:),'--')
xlabel('\eta')
ylabel('\theta(\eta)')
hold on
% saving the out put in text file for second solution
descris=[sol.x; sol.y];
save 'sliphybrid_lower.txt'descris -ascii
% Displaying the output for first solution
fprintf('\nSecond solution:\n');
fprintf('f"(0)=%7.9f\n',y(3));  % reduced skin friction 
fprintf('-theta(0)=%7.9f\n',-y(5)); %reduced local nusselt number
fprintf('Cfx=%7.9f\n',H6*(y(3)));    %  skin friction 
fprintf('Nux=%7.9f\n',-Kh*y(5));     % local nusselt number
fprintf('\n');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
end
% Define the ODE function
function f = OdeBVP(x,y,Pr,D1,Kh,H4,H3,S)
f =[y(2);y(3);(1/3)*D1*((y(2)^2)-2*(y(1)*y(3))+2*S);y(5);-2/3*(Pr*((H4/H3)/Kh)*y(1)*y(5))];
end
% Define the boundary conditions
function res = OdeBC(ya, yb, A, S, lambda)
res= [ya(1)-S;ya(2)-lambda;ya(4)-1;yb(3)-1;yb(4)];
end
% setting the initial guess for first solution
function v = OdeInit1(x,A,S,lambda)
v=[S+0.56;0;0;0;0];
end
% setting the initial guess for second solution
function v1 =OdeInit2(x, A, S,lambda)
v1 = [exp(-x);exp(-x);-exp(-x);-exp(-x);-exp(-x)];
end

[Torsten]

Since equations (1) - (3) don't depend on y(4) and y(5), I tested to solve them alone. But the same error message about the collocation equations pops up. So you can first restrict your search for possible errors in your code to equations (1) - (3).