Truncation versus mapping in the spectral approximation to the Korteweg-De Vries equation

We propose two different approaches to the numerical solution of the initial boundary value problem for the Korteweg-De Vries equation; the former is based on the truncation of the domain, the latter on the reduction of the real axis to a bounded interval by a suitable mapping technique. In both cases we consider spectral Chebyshev collocation methods for the space discretization and finite difference schemes for advancing in time. Both single and multi-domain approaches are discussed. We report numerical experiments showing the stability and convergence properties of the methods