How to numerically solve a reaction network with fast equilibrium steps? For example If I have to solve the following reaction numerically 

\begin{align}
*\ce{ + A(g) &amp;&lt;=&gt;[K1] [A*]} \tag{1}\\  
\ce{[A{*}] &amp;&lt;=&gt;[k1][k-1] [B{*}]} \tag{2}\\
\ce{[B*] &amp;&lt;=&gt;[K2] [B](g) +}* \tag{3}
\end{align}

Where the first and third reactions are fast equilibrium steps.

[* ] represents vacnt site and [A*]  and [B*] represent adsorbed species.

The reaction is carried out in a closed container, therefore the concentrations of A(g) and B(g) are not constant. 
Given initial A(g) and B(g) pressure and assuming zero coverage of reactants initially, how do I solve a system like this numerically.
For A adsorption:
$$r_1=0$$ 
because the reaction is in equilibrium.So,
$$K_1=\frac{[A]}{P_A \times [*]}$$
From this equation you can relate $[A]$ to $[*]$.Similarly, using the last reaction you can relate $[B]$ to $[*]$. Your [A] and [B] are connected via reaction 2.
$$\frac{d[A]}{dt}=-\frac{d[B]}{dt}=-k_1[A]+k_{-1}[B]$$
This is a first order differential equation, so you need only one boundary condition. You have three unknown and three boundary conditions $([A]_0=[B]_0=0$ and $[*]=1.00)$.