A numerical study for the KdV and the good Boussinesq equations using Fourier Chebyshev tau meshless method

DOI10.1007/s11075-013-9809-5zbMath1304.35598OpenAlexW2042296795MaRDI QIDQ483281

Wenting Shao, Xiong-Hua Wu

Publication date: 16 December 2014

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-013-9809-5

zbMATH Keywords

solitary wavesFourier spectral methodKorteweg-de Vries (KdV) equationChebyshev tau meshless method based on the highest derivativecomputational area moving techniquegood Boussinesq equation

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) KdV equations (Korteweg-de Vries equations) (35Q53) Soliton equations (35Q51) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items (5)

An integrable semi-discretization of the Boussinesq equation ⋮ New energy-preserving schemes using Hamiltonian boundary value and Fourier pseudospectral methods for the numerical solution of the ``good Boussinesq equation ⋮ A meshless finite point method for the improved Boussinesq equation using stabilized moving least squares approximation and Richardson extrapolation ⋮ Dynamic analysis of wave scenarios based on enhanced numerical models for the good Boussinesq equation ⋮ Optimal decay rates of the dissipative shallow water waves modeled by coupling the rosenau-RLW equation and the rosenau-Burgers equation with power of nonlinearity

Uses Software

• Matlab

Cites Work

• Chebyshev tau meshless method based on the highest derivative for fourth order equations
• A meshless based numerical technique for traveling solitary wave solution of Boussinesq equation
• A meshfree method for numerical solution of KdV equation
• A numerical method for KdV equation using collocation and radial basis functions
• Block-marching in time with DQ discretization: An efficient method for time-dependent problems
• A second order numerical scheme for the solution of the one-dimensional Boussinesq equation
• Differential quadrature and longterm integration
• On spectral approximations using modified Legendre rational functions: Application to the Korteweg-de Vries equation on the half line
• Spectral Methods
• Numerical Solutions of the Good Boussinesq Equation
• The Pseudospectral Method for Third-Order Differential Equations
• Spectral Methods in MATLAB
• An Algorithm for the Machine Calculation of Complex Fourier Series
• Exact N-soliton solutions of the wave equation of long waves in shallow-water and in nonlinear lattices

This page was built for publication: A numerical study for the KdV and the good Boussinesq equations using Fourier Chebyshev tau meshless method