Numerical solutions of the symmetric regularized-long-wave equation by trigonometric integrator pseudospectral discretization

TL;DR

This paper presents a spectral-order accurate numerical scheme using Fourier pseudospectral discretization and a trigonometric integrator for solving the symmetric regularized-long-wave equation, with applications to solitary wave collisions.

Contribution

It introduces a fully explicit, spectral-order accurate numerical method combining Fourier pseudospectral discretization with a trigonometric integrator for the SRLW equation.

Findings

The scheme achieves spectral accuracy in space and second-order accuracy in time.

Numerical experiments confirm the scheme's high accuracy and stability.

Simulations reveal interesting phenomena in solitary wave collisions.

Abstract

The computation of the symmetric regularized-long-wave (SRLW) equation, which describes weekly nonlinear ion acoustic and space-charge waves, is dealt with in this paper. The numerical scheme to be proposed applies the Fourier pseudospectral discretization to spatial derivatives in time space, with time advance accomplished in phase space by a integrator based on trigonometric polynomials which is fully explicit. Extensive numerical tests are reported, which are geared towards understanding the accuracy properties and studying the collisions of solitary waves in the SRLW. The results suggest that the scheme is of spectral-order accuracy in space and second-order accuracy in time. Also, some intriguing phenomena in the solitary wave collisions are observed in simulations.