A classical spectral approach based on the set of eigenfunctions of the Laplacian operator is proposed for the numerical solution of advection/diffusion/reaction equations for reactive mixing in 2-D laminar chaotic flows. This approach overcomes numerical diffusion problems and provides accurate spatiotemporal concentration fields in reasonable computer time up to very high values of Pe, such as Pe = 10(5) and higher. Moreover, a pseudo-spectral approach. combining spectral expansion with an FFT algorithm, provides an efficient computational strategy for both polynomial and non-polynomial nonlinearities such as those arising in non-isothermal reactive mixing problems with Arrhenius dependence of kinetic rates on temperature.