Trying to code from Polymath

this Polymath code into a Matlab code but I don't know how. Please I need to help. Please.......

[Juan Camilo Guerrero Paredes]

function A =function14(V,F)
A=zeros(6,1);

k1d = 0.25;
k2e = 0.10;
k3f = 5;

V=50;
v0=10;
tau= V/v0;
Ca0=1.5;
Cb0=2.0;
C_T0=3.5;

r1d = k1d*Ca*Cb^2;
r2e = k2e*Ca*Cd;
r3f = k3f*Cb*Cc^2;

ra = -r1d-3*r2e;
rb = -2*r1d-3*r3f;
rc = r1d+ r2e -2*r3f;
rd = r1d-2*r2e+r3f;
re = r2e;
rf = r3f;

F(1) = Ca-Ca0-ra*tau;
F(2) = Cb-Cb0-rb*tau;
F(3) = rc*tau-Cc;
F(4) = rd*tau-Cd;
F(5) = re*tau-Ce;
F(6) = rf*tau-Cf;

FT = F(1) + F(2) + F(3) + F(4) + F(5)+ F(6);

Ca = C_T0*(F(1)/ FT );
Cb = C_T0*(F(2)/ FT );
Cc = C_T0*(F(3)/ FT );
Cd = C_T0*(F(4)/ FT );


 A(1)=1;
 A(2)=1;
 A(3)=1;
 A(4)=1;
 A(5)=1;
 A(6)=1;

end

[Juan Camilo Guerrero Paredes]

Later I did this but dont work.

[V,F] = ode15s('Function14',[0 50],[ 15 , 20 , 0 , 0 , 0 , 0 ]);
v0 =10;
Ca0= 1.5;
La0= 1.5/v0;
Lb0= 2.0/v0;

Xa = (15-F(:,1))/15;
figure
plot(V,F(:,1),V,F(:,2),V,F(:,3),V,F(:,4),V,F(:,5),V,F(:,6))
 xlabel('Volumen (dm3)'),
 ylabel('Flujo molar (mol/s)')
 legend('Fa','Fb','Fc','Fd','Fe','Ff')

Answer 1

[Navya Singam]

Hi,

MATLAB Version of the Polymath code

%%Initial conditions
IC=[1,1,1,1,1,1];
Vspan=[0 50];

[V,CT]=ode15s(@fn,Vspan,IC);
%%Extracting the parameters
ca=CT(:,1);
cb=CT(:,2);
cc=CT(:,3);
cd=CT(:,4);
ce=CT(:,5);
cf=CT(:,6);

%Plot graph
figure
plot(V,ca,V,cb,V,cc,V,cd,V,ce,V,cf)
xlabel('Volume (dm3)')
ylabel('Flujo molar (mol/s)')
legend('Fa','Fb','Fc','Fd','Fe','Ff')
%ODE function
function dCTdV = fn(~,CT)
    %data
    V=50;
    v0=10;
    ca0=1.5;
    cb0=2.0;
    kd1=0.25;
    ke2=0.1;
    kf3=5;
    tau=V/v0;
    
    %extract parameters
    ca=CT(1);
    cb=CT(2);
    cc=CT(3);
    cd=CT(4);
    ce=CT(5);
    cf=CT(6);
    
    %supporting functions
    rd1=kd1*ca*cb^2;
    re2=ke2*ca*cd;
    rf3=kf3*cb*cc^2;
    ra=-rd1-3*re2;
    rb=-2*rd1-rf3;
    rc=rd1+re2-2*rf3;
    rd=rd1-2*re2+rf3;
    re=re2;
    rf=rf3;
    
    %odes
    dCTdV = [(ca-ca0-ra*tau);(cb-cb0-rb*tau);(rc*tau-cc);(rd*tau-cd);(tau*re-ce);(tau*rf-cf)];


end

Refer to this to know more about ode15s solver.

[Juan Camilo Guerrero Paredes]

Thanks very much. Navya Singam.....Thanks for helping me I try the code and it works I'm still learning about matLab. Greetings from Colombia.