A Legendre-pseudospectral method for computing travelling waves with corners (slope discontinuities) in one space dimension with application to Whitham's equation family
type: Item
instance of: scholarly article
title: A Legendre-pseudospectral method for computing travelling waves with corners (slope discontinuities) in one space dimension with application to Whitham's equation family
zbMATH Open document ID: 1027.65136
DOI: 10.1016/S0021-9991(03)00203-1
author: John P. Boyd
published in: Journal of Computational Physics
publication date: 2003-08-17T00:00:00Z
review text: The author proposes a Legendre-pseudospectral method for computing travelling waves with corners in one space dimension with application to Whitham's equation family. Because ``corner'' waves are not smooth, standard numerical methods converge poorly as the number of grid points is increased. He devises a Legendre-pseudospectral method which is uncorrupted by the singularity. A key step is to derive an extra boundary condition which uniquely identified the corner wave. Although his method is illustrated by the so-called ``Whitham's equation'', the ideas are widely applicable.
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 1965156
zbMATH Keywords: Corner waves
zbMATH Keywords: cnoidal waves
zbMATH Keywords: pseudospectral algorithm
zbMATH Keywords: Whitham equation
zbMATH Keywords: travelling waves with corners
reviewed by: Qin Meng Zhao
describes a project that uses: Differentiation Matrix Suite
MaRDI profile type: Publication
cites work: Q3661894
cites work: Q3207312
cites work: Solitons from sine waves: Analytical and numerical methods for non- integrable solitary and cnoidal waves
cites work: Peakons and coshoidal waves: Traveling wave solutions of the Camassa-Holm equation
cites work: Q4399935
cites work: Rational Chebyshev spectral methods for unbounded solutions on an infinite interval using polynomial-growth special basis functions
cites work: An integrable shallow water equation with peaked solitons
cites work: Q4311808
cites work: Q4039908
cites work: Nonlinear wave Packets of Equatorial Kelvin Waves
cites work: Q3862579
cites work: Terminal Damping of a Solitary Wave Due to Radiation in Rotational Systems
cites work: Q3033490
cites work: Critical thresholds in a convolution model for nonlinear conservation laws
cites work: Q4301170
cites work: Q4012057
cites work: Resonant Triads Involving a Nondispersive Wave
cites work: On nonanalytic solitary waves formed by a nonlinear dispersion.
cites work: A note on the breaking of waves
cites work: Quasiperiodic Solutions in Weakly Nonlinear Gas Dynamics. Part I. Numerical Results in the Inviscid Case
cites work: Q4096019
cites work: Variational methods and applications to water waves
cites work: Q4151274
full work available at URL: s0021-9991(03)00203-1
OpenAlex ID: W2090386765
description: scientific article; zbMATH DE number 1965156