A fast solver of Legendre-Laguerre spectral element method for the Camassa-Holm equation

DOI10.1007/S11075-020-01028-YzbMath1484.65278OpenAlexW3095504339MaRDI QIDQ2048813

Xueqin Ye, Zhong-qing Wang, Xu-hong Yu

Publication date: 24 August 2021

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

Full work available at URL: https://doi.org/10.1007/s11075-020-01028-y

zbMATH Keywords

numerical resultsCamassa-Holm equationdiagonalization techniqueLegendre-Laguerre spectral element method

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

Related Items (4)

An efficient Fourier-Laguerre spectral-Galerkin method for exterior problems of two-dimensional complex obstacles ⋮ Generalized Bernoulli-Laguerre polynomials: applications in coupled nonlinear system of variable-order fractional PDEs ⋮ Error estimates of invariant-preserving difference schemes for the rotation-two-component Camassa-Holm system with small energy ⋮ A Legendre dual-Petrov-Galerkin spectral element method for the Kawahara-type equations

Cites Work

• Unnamed Item
• Unnamed Item
• Spectral element method for mixed inhomogeneous boundary value problems of fourth order
• Multi-symplectic wavelet collocation method for the nonlinear Schrödinger equation and the Camassa-Holm equation
• Geometric finite difference schemes for the generalized hyperelastic-rod wave equation
• Spectral method for differential equations of degenerate type on unbounded domains by using generalized Laguerre functions
• Multi-symplectic integration of the Camassa-Holm equation
• An explicit finite difference scheme for the Camassa-Holm equation
• A fully diagonalized spectral method using generalized Laguerre functions on the half line
• Diagonalized Legendre spectral methods using Sobolev orthogonal polynomials for elliptic boundary value problems
• The Cauchy problem for an integrable shallow-water equation
• Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation
• Linear and Hamiltonian-conserving Fourier pseudo-spectral schemes for the Camassa-Holm equation
• Numerical study of traveling-wave solutions for the Camassa--Holm equation
• Numerical simulation of Camassa-Holm peakons by adaptive upwinding.
• Generalized Laguerre approximations and spectral method for the Camassa–Holm equation
• Efficient Spectral and Spectral Element Methods for Eigenvalue Problems of Schrödinger Equations with an Inverse Square Potential
• Spectral Methods
• A Local Discontinuous Galerkin Method for the Camassa–Holm Equation
• A Triangular Spectral Element Method Using Fully Tensorial Rational Basis Functions
• A Convergent Finite Difference Scheme for the Camassa–Holm Equation with General $H^1$ Initial Data
• Spectral Methods and Their Applications
• An integrable shallow water equation with peaked solitons
• Geometric Numerical Integration for Peakon b-Family Equations
• Spectral Methods
• Convergence of a spectral projection of the Camassa‐Holm equation
• Convergence of a Finite Difference Scheme for the Camassa–Holm Equation

This page was built for publication: A fast solver of Legendre-Laguerre spectral element method for the Camassa-Holm equation