How to define the variables of a function handle before the function

Hello I am trying to get this to work by defining S as y(1) before putting it in S,I,R then F.

Please let me know what is the issue, It was working but i changed something and it doesn't work anymore.

It gives me this error:

Unrecognized function or variable 'y'.

Error in Sc (line 14)

S = y(1)

B=0.02818;
L=0.00098;
h=1;
t_max=5;
t_span = (0:h:t_max);

S_0=2782000
I_0=1;
R_0=0;
y0 = [S_0;I_0;R_0];
N = S_0+I_0+R_0


S = y(1)
I = y(2)
R = y(3)
 
 S_t = - (B*I*S)/N
 I_t = (B*I*S)/N - L*I
 R_t = L*I


F = @(t,y) [ (B*y(2)*y(1))/N ; (B*y(2)*y(1))/N ;-L*I];

[t,y]= ode45(F,t_span,y0);

[John D'Errico]

Regardless of what you had working, you cannot alias variables together, so that when one changes, the other also changes. (Ok, not easily, you could possibly do it with a custom class. Nasty code though, and just pleading for bugs.)

Answer 1

[Walter Roberson]

B=0.02818;
L=0.00098;
h=1;
t_max=5;
t_span = (0:h:t_max);

S_0=2782000
I_0=1;
R_0=0;
y0 = [S_0;I_0;R_0];
N = S_0+I_0+R_0


S = @(y) y(1)
I = @(y) y(2)
R = @(y) y(3)
 
 S_t = @(y) - (B*I(y)*S(y))/N
 R_t = L*I(y)
 I_t = @(y) (B*I(y)*S(y))/N - R_t(y)



F = @(t,y) [ -S_t(y); I_t(y) + R_t(y); -R_t(y)];

[t,y]= ode45(F,t_span,y0);

This will have notably worse performance than your existing F definition, due to the extra layers of function calls.

If you want to define your ode function in expressions that are more clear than your existing F, then I recommend using the Symbolic Toolbox to express them, and follow the workflow in the first example of odeFunction() to convert them for numeric use.