A novel linearized and momentum‐preserving Fourier pseudo‐spectral scheme for the <scp>Rosenau‐Korteweg</scp> de Vries equation

In this article, we design a novel linearized and momentum-preserving Fourier pseudo-spectral scheme to solve the Rosenau-Korteweg de Vries equation. With aid of new semi-norm equivalence between method finite difference method, prior bound numerical solution in discrete L ∞ $$ {L}^{\infty } -norm is obtained from momentum conservation law. Subsequently, based on energy solution, show that, without any restriction mesh ratio, convergent with order O N − s + τ 2 O\left({N}^{-s}+{\tau}^2\right) -norm, where number collocation points used spectral \tau time step. Numerical results are addressed confirm our theoretical analysis.