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

Abstract

The aim of this work is to provide an e±cient technique for numerical solutions of the reaction–dispersion equations including convection and di®usion. 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 e±ciently catch such challenging physical behavior. Quantitative convergence results in both time and space are illustrated for the reaction–dispersion problems. © 2022 Elsevier B.V., All rights reserved.