About this scholarly article

A novel linearized and momentum-preserving Fourier pseudo-spectral scheme for the Rosenau-Korteweg de Vries equation by Jiang, Chaolong; Cui, Jin; Cai, Wenjun; Wang, Yushun is a scholarly article available to read on EtoBox.

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

Author

Jiang, Chaolong; Cui, Jin; Cai, Wenjun; Wang, Yushun

Published

2019

Language

EN