For an arbitrarily complex surface reaction mechanism, it can be difficult to provide an initial set of surface site fractions and gas-phase mass fractions at the surface, which satisfies Equation 12–19 , Equation 12–20 , Equation 12–21 and Equation 12–22 at . This self-consistency is necessary because the equations for the surface site fractions and gas-phase mole fractions at the walls are actually algebraic equations, rather than ordinary differential equations. For the solution to begin smoothly, it is necessary to satisfy exactly the algebraic equations at . To this end, a solution is first determined for the correct set of and that satisfy these boundary condition equations at the channel inlet. This procedure employs the numerical software Twopnt to solve for the self-consistent set of gas-phase and surface concentrations at each wall. The user can optionally give the Twopnt procedure initial guesses for the gas-phase and surface concentrations to aid in the convergence. The initial Twopnt problem can also be bypassed altogether if the self-consistent values for the and are supplied by the user.