What changes are needed to run the code

Psi = pi/2; L1 = 0.1; L2 = 0.1; L = 0.1; Pr = 1; M = 5; 
Ec = 0.5; Nb = 0.5; Nt = 0.1; fw = 0.5; Q = 0.1; Le = 2; Kc = 1;
A = linspace(-1,1,101);
for L = [1 2 3]/10
    BC = @(ya,yb)[ ya(1)-fw; ya(2)+1; ya([4;7])-1; yb([2;4;6]) ];
    ODE = @(x,y)[   y(2); y(3); ( A.*(y(2)+(1/2)*x*y(3)) - y(1)*y(3) + y(2)*( y(2)+M^2*(sin(Psi))^2) - L1*y(4) - L2*y(6))/(1+(1/L)); 
        y(5);  -Pr*( y(1)*y(5) - (1/2)*A.*x*y(5) + Nb*y(5)*y(7) + Nt*y(5)^2 + M^2*Ec*y(2)^2+Q*y(4) );
        y(7);  -Le*Pr*( y(1)*y(7)-(1/2)*A.*x*y(7)-Kc*y(6) ) - (Nt/Nb)*(-Pr*( y(1)*y(5) - (1/2)*A.*x*y(5) + Nb*y(5)*y(7) + Nt*y(5)^2 + M^2*Ec*y(2)^2+Q*y(4) ))  ];
    xa = 0; xb = 6; xn = linspace(xa,xb,101); x = xn; solinit = bvpinit(x,[0 1 0 1 0 1 0]); sol = bvp5c(ODE,BC,solinit);  
    S = deval(sol,x); f0 = deval(sol,xa);  
    figure(1);plot(A,S(2,:),'-','LineWidth',2);xlabel('\bf\eta','color','b'); ylabel('\bff^\prime(\eta)','color','b');hold on,
end

Error using vertcat
Dimensions of arrays being concatenated are not consistent.

Error in solution (line 6)
ODE = @(x,y)[ y(2); y(3); ( A.*(y(2)+(1/2)*x*y(3)) - y(1)*y(3) + y(2)*( y(2)+M^2*(sin(Psi))^2) - L1*y(4) - L2*y(6))/(1+(1/L));

Error in bvparguments (line 105)
testODE = ode(x1,y1,odeExtras{:});

Error in bvp5c (line 129)
bvparguments(solver_name,ode,bc,solinit,options);

%% ERROR is:

Dimensions of matrices being concatenated are not consistent.

%% Help needed to run

Answer 1

[Jan]

ODE = @(x,y) [ ...
    y(2); ...
    y(3); ...
    (A.*(y(2)+0.5*x*y(3)) - y(1)*y(3) + y(2)*( y(2)+M^2*(sin(Psi))^2) - L1*y(4) - L2*y(6))/(1+(1/L)); ...
    y(5); ...
    -Pr*(y(1)*y(5) - 0.5*A.*x*y(5) + Nb*y(5)*y(7) + Nt*y(5)^2 + M^2*Ec*y(2)^2+Q*y(4)); ...
    y(7); ...
    -Le*Pr*(y(1)*y(7) - 0.5*A.*x*y(7)-Kc*y(6)) - (Nt/Nb)*(-Pr*(y(1)*y(5) - 0.5*A.*x*y(5) + Nb*y(5)*y(7) + Nt*y(5)^2 + M^2*Ec*y(2)^2+Q*y(4)))];

Yes, the 3rd, 5th and 7th element have the size 1x101, while the others are scalars. This comes from the vector A. I cannot guess, what you want to do instead.

[MINATI PATRA]

Hi Jan

Actually I am trying to draw S(2,:) w.r.t A ( varies in x-axis ) for different values of L = [1 2 3]/10

i.e. plot(A,S(2,:))

[Jan]

Then you have to run the integration for all values of A. You cannot find all different trajectories with one integration.

Psi = pi/2;
L1 = 0.1;
L2 = 0.1;
L = 0.1;
Pr = 1;
M = 5; 
Ec = 0.5;
Nb = 0.5;
Nt = 0.1;
fw = 0.5;
Q = 0.1;
Le = 2;
Kc = 1;
A = linspace(-1, 1, 10);
xa = 0;
xb = 6;
xn = linspace(xa,xb,101);
x  = xn;
figure;
axesH = axes('NextPlot', 'add');
for L = [1 2 3]/10
    for iA = A
       BC = @(ya,yb)[ ya(1)-fw; ya(2)+1; ya([4;7])-1; yb([2;4;6]) ];
       ODE = @(x,y) [ ...
                y(2); ...
                y(3); ...
                (iA.*(y(2)+0.5*x*y(3)) - y(1)*y(3) + y(2)*( y(2)+M^2*(sin(Psi))^2) - L1*y(4) - L2*y(6))/(1+(1/L)); ...
                y(5); ...
                -Pr*(y(1)*y(5) - 0.5*iA.*x*y(5) + Nb*y(5)*y(7) + Nt*y(5)^2 + M^2*Ec*y(2)^2+Q*y(4)); ...
                y(7); ...
                -Le*Pr*(y(1)*y(7) - 0.5*iA.*x*y(7)-Kc*y(6)) - (Nt/Nb)*(-Pr*(y(1)*y(5) - 0.5*iA.*x*y(5) + Nb*y(5)*y(7) + Nt*y(5)^2 + M^2*Ec*y(2)^2+Q*y(4)))];
        solinit = bvpinit(x, [0 1 0 1 0 1 0]);
        sol = bvp5c(ODE, BC, solinit);  
        S   = deval(sol, x);
        f0  = deval(sol, xa);  
        plot(axesH, iA, S(2,:), '.', 'LineWidth', 2);
    end
end
xlabel('\bf\eta','color','b');
ylabel('\bff^\prime(\eta)','color','b');

I assume you want to modify the oputput. Maybe collect the different output of S(:,2) in an array at first and draw it as plot(A, collectedS)?

[MINATI PATRA]

@ Dear Jan

Thanks for your try. But unfortunately Your attempt is not upto mark (I may be wrong).

Please have a look into my trial. It gives so many curves instead of THREE. Can it be modified?

A = -0.50; Psi = pi/2; L1 = 0.1; L2 = 0.1; L = 0.1; Pr = 2; M = 5;

Ec = 0.5; Nb = 0.5; Nt = 0.1; fw = 0.5; Q = 0.1; Le = 2; Kc = 1;

Av = linspace(-1,1,101);

for M = [1 2 3]

for i = 1:length(Av)

A = Av(i);

BC = @(ya,yb)[ ya(1)-fw; ya(2)+1; ya([4;7])-1; yb([2;4;6]) ];

ODE = @(x,y)[ y(2); y(3); ( A.*(y(2)+(1/2)*x*y(3)) - y(1)*y(3) + y(2)*( y(2)+M^2*(sin(Psi))^2) - L1*y(4) - L2*y(6))/(1+(1/L));

y(5); -Pr*( y(1)*y(5) - (1/2)*A.*x*y(5) + Nb*y(5)*y(7) + Nt*y(5)^2 + M^2*Ec*y(2)^2+Q*y(4) );

y(7); -Le*Pr*( y(1)*y(7)-(1/2)*A.*x*y(7)-Kc*y(6) ) - (Nt/Nb)*(-Pr*( y(1)*y(5) - (1/2)*A.*x*y(5) + Nb*y(5)*y(7) + Nt*y(5)^2 + M^2*Ec*y(2)^2+Q*y(4) )) ];

xa = 0; xb = 6; xn = linspace(xa,xb,101); x = xn; solinit = bvpinit(x,[0 1 0 1 0 1 0]); sol = bvp5c(ODE,BC,solinit);

S = deval(sol,x); f0 = deval(sol,xa); Cf = (1+(1/L))*f0(3); Nu = - f0(5); Sh = - f0(7);

figure(41); plot(Av,S(2,:),'LineWidth',2); xlabel('\bfA','color','b'); ylabel('\bff^\prime(\eta)','color','b'); hold on,

end

end

[Jan]

Please use the tools in the forum to format your code. This improves the readability.

Why do you expect 3 curves only?

[MINATI PATRA]

Dear Jan Since I have taken 3 values of the parameter L And variations of A will be in X axis

[MINATI PATRA]

Dear Jan

This is still unsolved.

Can it be possible for a last try?

[Jan]

I'm not sure, which problem is still open. The code of my answer is running, and only the diagram looks a little bit strange. I do not know, what you want to get instead of this solution. So please explain again, what is still unsolved.