A space-time Chebyshev spectral collocation method for the reaction-dispersion equations with anti-kink-type waves

The aim of this work is to provide an efficient technique for numerical solutions of the reaction-dispersion equations including convection and diffusion. The Chebyshev spectral collocation method (ChSCM) is used in both space and time to exhibit anti-kink-type waves that appear as the result of the proposed model equations. It is shown that the revealed solutions are promising to efficiently catch such challenging physical behavior. Quantitative convergence results in both time and space are illustrated for the reaction-dispersion problems.