Undefined function or variable using ODE45

I'm having trouble with defining an independent variable in matlab. I am getting the error, 'undefined function or variable 'Y'. Y is the variable I am trying to solve for.

%elementary rate law
FA0=10; %mol/min
W=100; %KG
a=.008; %kg^-1
k1C=2; %L/kg cat/min
K1C=.2; %mol/L
k2D=.4; %L/kg cat/min
k3E=5; %L/mol^2/kg cat/min
kc=1; %L/kg cat/min
v=16.67; %L/min
Fa=Y(1);
Fb=Y(2);
Fc=Y(3);
Fd=Y(4);
Fe=Y(5);
y=Y(6);

CT0=FA0;
FT=Fa+Fb+Fc+Fd+Fe;
Ca=CT0*(Fa/FT)*y;
Cb=CT0*(Fb/FT)*y;
Cc=CT0*(Fc/FT)*y;
Cd=CT0*(Fd/FT)*y;
Ce=CT0*(Fe/FT)*y;

r1C=k1C*(Ca-(Cb*Cc/K1C));
r2D=k2D*Cd;
r3E=k3E*Cd*(Ce^2);

ra=-r1C-r2D;
rb=r1C;
rc=r1C-r3E;
rd=r2D-.5*r3E;
re=r3E;

dFadw=ra;
dFbdw=rb;
dFcdw=rc;
dFddw=rd;
dFedw=re;
dydw=-a*FT/(2*FT0*y);

fun=@(w,Y)[dFadw;dFbdw;dFcdw;dFddw;dFedw,dydw];
wspan=0:1:100;
x0=[10;0;0;0;0;1];
[T,X] = ode45(fun,wspan,x0)

Answer 1

[Star Strider]

I believe this is what you actually intend:

function dy = fun(T,Y)
FT0 = 42;
FA0=10; %mol/min
W=100; %KG
a=.008; %kg^-1
k1C=2; %L/kg cat/min
K1C=.2; %mol/L
k2D=.4; %L/kg cat/min
k3E=5; %L/mol^2/kg cat/min
kc=1; %L/kg cat/min
v=16.67; %L/min
Fa=Y(1);
Fb=Y(2);
Fc=Y(3);
Fd=Y(4);
Fe=Y(5);
y=Y(6);
CT0=FA0;
FT=Fa+Fb+Fc+Fd+Fe;
Ca=CT0*(Fa/FT)*y;
Cb=CT0*(Fb/FT)*y;
Cc=CT0*(Fc/FT)*y;
Cd=CT0*(Fd/FT)*y;
Ce=CT0*(Fe/FT)*y;
r1C=k1C*(Ca-(Cb*Cc/K1C));
r2D=k2D*Cd;
r3E=k3E*Cd*(Ce^2);
ra=-r1C-r2D;
rb=r1C;
rc=r1C-r3E;
rd=r2D-.5*r3E;
re=r3E;
dFadw=ra;
dFbdw=rb;
dFcdw=rc;
dFddw=rd;
dFedw=re;
dydw=-a*FT/(2*FT0*y);
dy = [dFadw;dFbdw;dFcdw;dFddw;dFedw;dydw];
end

wspan=0:1:100;
x0=[10;0;0;0;0;1];
[T,X] = ode45(@fun,wspan,x0);

figure
plot(T,X)
grid

The ‘FT0’ value and assignment are missing, so I created one to test the code. (You may want to substitute a different value.) This runs without error.

[Andrew Knight]

Thank you. I've put in the value of .6 for CT0, but now the code takes forever to run. It has been running for 10 min so far. Is this just becuase I have 6 equations with 6 unknowns? Is there any way to optimize this?

[Andrew Knight]

Nevermind, I had some incorrect values. Your fix worked, thanks!

[Star Strider]

As always, my pleasure!