NDSolve: Boundary conditions not numerical

Question

I am trying to solve coupled differential equations using NDsolve. I am getting an error which says Boundary conditions not numerical. I am not sure about my mistake. Can I get some help? My code is as follows

        `

    a = 1*10^10;
    b = -2*10^7;
    n = 11167.3;
    Subscript[L, i] = 0.4814*10^-3;
    Subscript[z, 1] = 0.25*10^-3;
    Subscript[z, 2] = 1.75*10^-3;
    a1 = 1;


    q[z_] := a*z^2 + b*z + n;(*Functional form of \[CapitalDelta]\[Beta]*)

    g = \[Pi]/Subscript[L, i];(*Subscript[\[CapitalDelta]\[Beta], NA]*)
    \[Kappa][z_, c_] := 
     c*(g - q[z]);(*constant\[Times](Subscript[\[CapitalDelta]\[Beta], \
    NA]-Subscript[\[CapitalDelta]\[Beta], MAX])*)
    eq1[z_, c_] := Ar1'[z] == I*\[Kappa][z, c]*Ar2[z, c]*Exp[-I*q[z]*z]
    eq2[z_, c_] := Ar2'[z] == I*\[Kappa][z, c]*Ar1[z, c]*Exp[+I*q[z]*z]
    syst = NDSolve[{eq1[z, c], eq2[z, c], Ar1[Subscript[z, 1]] == 1, 
       Ar2[Subscript[z, 2]] == 0}, {Ar1, Ar2}, {z, Subscript[z, 1], 
       Subscript[z, 2]}, {c, 0, 2}, MaxSteps -> \[Infinity]]

Answer 1

All these problems can be easily found if each statement is evaluated on its own and by looking at the output before going to the next statement. Then you'd see what the problem is instead of throwing all the code into one statement which makes it hard to see what is wrong

a = 3*10^10
b = -1*10^7
c = 11167.3
Subscript[L, i] = 0.4814*10^-3
Subscript[z, 1] = 0.25*10^-3
Subscript[z, 2] = 1.75*10^-3
q[z_] := a*z^2 + b*z + c
g = \[Pi]/Subscript[L, i]
\[Kappa][z_] := n*(g - q[z])

So far OK. Now the next one

bc = {Ar1[Subscript[z, 1]] == a1, Ar2[Subscript[z, 2]] == 0}

Opps, we already see something wrong. What is a1? Now the next one

ode = {Ar1'[z] == I*\[Kappa][z]*Ar2[z]*Exp[-I*q[z]*z], 
  Ar2'[z] == I*\[Kappa][z]*Ar1[z]*Exp[+I*q[z]*z]}

Opps, we see anther problem. What is n in there? it has no value. Next

 syst = NDSolve[{ode, bc}, {Ar1, Ar2}, {z, Subscript[z, 1], Subscript[z, 2]}]

Gives the errors you mentioned. So from the above, it is clear what the error is. You need numerical values for n and a1

a1 = 1; n = 1;
syst = NDSolve[{ode, bc}, {Ar1, Ar2}, {z, Subscript[z, 1], Subscript[z, 2]}]