solve bvp using bvp4c

function ModifiedHNF()
global C1
global C2
format long
solinit=bvpinit(linspace(0,4,3),[0,0,0,0,0]);
sol=bvp4c(@deriv,@bcs,solinit);
x = linspace(0,4);
y = deval(sol,x);
% plot(sol.x,sol.y(1,:),'r-');
plot(x,y(1,:),'r-');
end

function dydx = deriv(~,y)

Pr=6.2;
phi_1=[0 0.10 0.50];
phi_2=[0 0.01 0.10];
C1=(1-phi_1).*(1-phi_2)+(((1-phi_2).*(phi_1.*3970)+(phi_2.*8933))/997.1);
C2=(1-phi_1).*(1-phi_2)+((1-phi_2).*phi_1.*(3970*765)+phi_2.*(8933*385))/(997.1*4179);
knf=(40+(2.*0.613)-(2.*phi_1).*(0.613-40)).*(0.613)/(40+(2.*0.613)+(phi_1)*(0.613-40));
khnf=(400+(2.*knf)-(2.*phi_2).*(knf-400)).*(knf)/(400+(2.*knf)+(phi_2).*(knf-400));

dydx = [y(2);
        y(3);
       -C1.*(y(1).*y(3)-y(2).*y(2)).*(1-phi_1).^(2.5).*(1-phi_2).^(2.5);
        y(5);
       -C2.*Pr.*(y(1).*y(5).*0.613)/khnf];

end
 
function res = bcs(ya,yb)
S=0;
Lambda=1;
Bi=[0.5 1 20];
res = [ ya(1)-S;
        ya(2)- Lambda;
        ya(5)+((0.613/khnf)*Bi*(1-ya(4)));
        yb(2);
        yb(4)];
end

this is the code to solve bvp using bvp4c where i have 5 odes. however, it shows an error in command window.

it says Error in ModifiedHNF (line 7)

sol=bvp4c(@deriv,@bcs,solinit);

[MOSLI KARIM]

Here is the correction to your code

function ModifiedHNF()

global Pr phi_1 phi_2 C1 C2 knf khnf Lambda S Bi

Pr = 6.2;

S = 0;

Lambda = 1;

Bi = 0.5;

% Cell array pour stocker les noms de couleur

colors = {'r', 'g', 'b', 'c', 'm', 'k'};

% Cell array pour stocker les noms de la légende

legend_names = {};

for phi_1 = [0 0.10 0.50]

for phi_2 = [0 0.01 0.10]

C1 = (1 - phi_1) * (1 - phi_2) + (((1 - phi_2) * (phi_1 * 3970) + (phi_2 * 8933)) / 997.1);

C2 = (1 - phi_1) * (1 - phi_2) + ((1 - phi_2) * phi_1 * (3970 * 765) + phi_2 * (8933 * 385)) / (997.1 * 4179);

knf = (40 + (2 * 0.613) - (2 * phi_1) * (0.613 - 40)) * (0.613) / (40 + (2 * 0.613) + (phi_1) * (0.613 - 40));

khnf = (400 + (2 * knf) - (2 * phi_2) * (knf - 400)) * (knf) / (400 + (2 * knf) + (phi_2) * (knf - 400));

solinit = bvpinit(linspace(0, 4, 3), [0, 0, 0, 0, 0]);

sol = bvp4c(@deriv, @bcs, solinit);

x = linspace(0, 4);

y = deval(sol, x);

figure(1)

hold on

% Utiliser le modulo (%) pour garantir que le compteur reste dans la plage des indices valides

color_index = mod(length(legend_names), length(colors)) + 1;

plot(x, y(1, :), colors{color_index});

% Ajouter le nom de la combinaison de phi_1 et phi_2 à la légende

legend_names{end+1} = ['\phi_1=' num2str(phi_1) ', \phi_2=' num2str(phi_2)];

end

end

% Ajouter la légende

legend(legend_names);

function dydx = deriv(~, y)

dydx = [y(2);

y(3);

-C1 * (y(1) * y(3) - y(2) * y(2)) * (1 - phi_1)^(2.5) * (1 - phi_2)^(2.5);

y(5);

-C2 * Pr * (y(1) * y(5) * 0.613) / khnf];

end

function res = bcs(ya, yb)

res = [ya(1) - S;

ya(2) - Lambda;

ya(5) + ((0.613 / khnf) * Bi * (1 - ya(4)));

yb(2);

yb(4)];

end

end