New energy-preserving algorithms for nonlinear Hamiltonian wave equation equipped with Neumann boundary conditions
type: Item
instance of: scholarly article
title: New energy-preserving algorithms for nonlinear Hamiltonian wave equation equipped with Neumann boundary conditions
zbMATH Open document ID: 1429.65189
author: Wei Shi
author: Changying Liu
author: Xinyuan Wu
published in: Applied Mathematics and Computation
publication date: 2019-11-22T00:00:00Z
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 35C15
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 35L71
zbMATH DE Number: 7135003
zbMATH Keywords: nonlinear Hamiltonian wave equation
zbMATH Keywords: finite difference discretization
zbMATH Keywords: Neumann boundary conditions
zbMATH Keywords: energy-preserving algorithm
zbMATH Keywords: AVF formula
zbMATH Keywords: oscillatory system
describes a project that uses: LIMbook
MaRDI profile type: Publication
full work available at URL: j.amc.2018.07.059
OpenAlex ID: W2887840168
cites work: A numerical method for the one-dimensional sine-Gordon equation
cites work: On the numerical solution of the Klein‐Gordon equation
cites work: Efficient implementation of Gauss collocation and Hamiltonian boundary value methods
cites work: Energy conservation issues in the numerical solution of the semilinear wave equation
cites work: Line Integral Methods for Conservative Problems
cites work: Hamiltonian Boundary Value Methods (Energy Conserving Discrete Line Integral Methods)
cites work: A simple framework for the derivation and analysis of effective one-step methods for ODEs
cites work: A note on the efficient implementation of Hamiltonian BVMs
cites work: Energy- and Quadratic Invariants--Preserving Integrators Based upon Gauss Collocation Formulae
cites work: Q4822032
cites work: Preserving energy resp. dissipation in numerical PDEs using the ``Average Vector Field'' method
cites work: Energy preserving schemes for nonlinear Hamiltonian systems of wave equations: application to the vibrating piano string
cites work: An algebraic approach to invariant preserving integators: the case of quadratic and Hamiltonian invariants
cites work: Fourth-order compact solution of the nonlinear Klein-Gordon equation
cites work: Lie-Poisson Hamilton-Jacobi theory and Lie-Poisson integrators
cites work: A Legendre spectral method for solving the nonlinear Klein-Gordon equation
cites work: Geometric Numerical Integration
cites work: On energy conservation of the simplified Takahashi-Imada method
cites work: Numerical simulation for a nonlinear partial differential equation with variable coefficients by means of the discrete variational derivative method
cites work: B-series methods cannot be volume-preserving
cites work: Preserving algebraic invariants with Runge-Kutta methods
cites work: Derivation of the discrete conservation laws for a family of finite difference schemes
cites work: Analysis of four numerical schemes for a nonlinear Klein-Gordon equation
cites work: Finite Difference Calculus Invariant Structure of a Class of Algorithms for the Nonlinear Klein–Gordon Equation
cites work: An extended discrete gradient formula for oscillatory Hamiltonian systems
cites work: An efficient high-order explicit scheme for solving Hamiltonian nonlinear wave equations
cites work: The boundness of the operator-valued functions for multidimensional nonlinear wave equations with applications
cites work: Arbitrarily high-order time-stepping schemes based on the operator spectrum theory for high-dimensional nonlinear Klein-Gordon equations
cites work: Large amplitude instability in finite difference approximations to the Klein-Gordon equation
cites work: Geometric integration using discrete gradients
cites work: Linearization-preserving self-adjoint and symplectic integrators
cites work: High-order compact solution of the one-dimensional heat and advection-diffusion equations
cites work: High-order solution of one-dimensional sine-Gordon equation using compact finite difference and DIRKN methods
cites work: A new class of energy-preserving numerical integration methods
cites work: Multi-symplectic Runge-Kutta collocation methods for Hamiltonian wave equations
cites work: Q3782682
cites work: Numerical solution of a nonlinear Klein-Gordon equation
cites work: Product Approximation for Nonlinear Klein-Gordon Equations
cites work: A new high precision energy-preserving integrator for system of oscillatory second-order differential equations
cites work: Structure-Preserving Algorithms for Oscillatory Differential Equations II
cites work: Efficient energy-preserving integrators for oscillatory Hamiltonian systems
cites work: Structure-Preserving Algorithms for Oscillatory Differential Equations
Wikidata QID: Q129369352
DOI: 10.1016/J.AMC.2018.07.059
description: scientific article; zbMATH DE number 7135003