A mathematical model for an automotive three-way catalytic converter based on experimental mechanistic kinetics is developed. The transient model includes a one-space dimension discretization for the gas phase and a two-dimensional discretization for the solid phase is comprised of the washcoat and substrate. Axi-symmetry is assumed. The combination of the complex kinetic model and the associated transport equations generates a large system of non-linear equations that is solved using the Newton-Krylov method based on a pre-conditioned GMRES algorithm. Simulated light-off curves for cold start operation illustrate the importance of including dynamic adsorption process in the model for this type of operating condition. Diffusion limitation in the washcoat is shown to be very significant even at relatively low operating temperatures. From the numerical standpoint, the importance of the choice of pre-conditioner is demonstrated. The use of parallel computing at a fine grain level on vector-vector and vector-matrix operation is shown to provide a large degree of speedup, which increases as the number of grid points increases.