Error estimates for a fully discrete spectral scheme for nonlinear Boussinesq systems
type: Item
instance of: scholarly article
title: Error estimates for a fully discrete spectral scheme for nonlinear Boussinesq systems
zbMATH Open document ID: 1493.65169
author: Yanyan Li
published in: Numerische Mathematik
publication date: 2022-01-19T00:00:00Z
review text: A high-order fully discrete numerical scheme is developed for the solution of the initial-periodic boundary value problem for a nonlinear family of Boussinesq systems by combining a Fourier collocation spectral approximation in space and the classical fourth-order Runge-Kutta scheme for the time discretization. The error bounds have spectral accuracy in space and optimal order in time. Numerical experiments are shown to validate the accuracy of method and the convergence rate. Furthermore, the solitary waves and their interactions are studied numerically.
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 76B15
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35C08
zbMATH DE Number: 7459673
zbMATH Keywords: nonlinear Boussinesq systems
zbMATH Keywords: Fourier collocation method
zbMATH Keywords: Runge-Kutta scheme
reviewed by: Bülent Karasözen
MaRDI profile type: Publication
full work available at URL: s00211-021-01239-y
OpenAlex ID: W3211287150
cites work: Q4581148
cites work: Error estimates for Galerkin approximations of the “classical” Boussinesq system
cites work: Numerical solution of the `classical' Boussinesq system
cites work: Numerical solution of Boussinesq systems of the Bona-Smith family
cites work: Numerical Methods for Evolutionary Differential Equations
cites work: Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media. I: Derivation and linear theory
cites work: Numerical solution of KdV-KdV systems of Boussinesq equations. I: The numerical scheme and generalized solitary waves
cites work: A Boussinesq system for two-way propagation of nonlinear dispersive waves
cites work: A model for the two-way propagation of water waves in a channel
cites work: Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media: II. The nonlinear theory
cites work: Spectral Methods
cites work: Exact traveling-wave solutions to bidirectional wave equations
cites work: The second law of thermodynamics and stability
cites work: Boussinesq systems of Bona-Smith type on plane domains: theory and numerical analysis
cites work: Stability and convergence analysis of fully discrete Fourier collocation spectral method for 3-D viscous Burgers' equation
cites work: Spectral Methods for Time-Dependent Problems
cites work: Fourier analysis and partial differential equations
cites work: Analysis and computation of a nonlinear Korteweg-de Vries system
cites work: Stability of the fourth order Runge-Kutta method for time-dependent partial differential equations
cites work: Convergence of Fourier Methods for the Navier–Stokes Equations
cites work: Stability analysis for a fully discrete spectral scheme for Boussinesq systems
DOI: 10.1007/S00211-021-01239-Y
description: scientific article; zbMATH DE number 7459673