A fourth-order AVF method for the numerical integration of sine-Gordon equation

DOI10.1016/j.amc.2017.05.055zbMath1426.37050OpenAlexW2621463890MaRDI QIDQ1740038

Xianqiang Yang

Publication date: 29 April 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2017.05.055

zbMATH Keywords

solitonpseudo-spectral methodsine-Gordon equationaverage vector field methodenergy-preserving

Mathematics Subject Classification ID

Related Items (16)

The Hamiltonian structure and fast energy-preserving algorithms for the fractional Klein-Gordon equation ⋮ Arbitrarily high‐order accurate and energy‐stable schemes for solving the conservative Allen–Cahn equation ⋮ Energy-preserving Du Fort-Frankel difference schemes for solving sine-Gordon equation and coupled sine-Gordon equations ⋮ Efficient energy-preserving eighth-order compact finite difference schemes for the sine-Gordon equation ⋮ Padé schemes with Richardson extrapolation for the sine-Gordon equation ⋮ A conservative difference scheme for the Riesz space-fractional sine-Gordon equation ⋮ Numerical inverse scattering for the sine-Gordon equation ⋮ A fourth-order conservative difference scheme for the Riesz space-fractional sine-Gordon equations and its fast implementation ⋮ Legendre spectral element method for solving sine-Gordon equation ⋮ An explicit fourth-order energy-preserving difference scheme for the Riesz space-fractional sine-Gordon equations ⋮ A family of effective structure-preserving schemes with second-order accuracy for the undamped sine-Gordon equation ⋮ Padé numerical schemes for the sine-Gordon equation ⋮ A stable time-space Jacobi pseudospectral method for two-dimensional sine-Gordon equation ⋮ A linearly implicit and local energy-preserving scheme for the sine-Gordon equation based on the invariant energy quadratization approach ⋮ Numerical solution of two-dimensional nonlinear sine-Gordon equation using localized method of approximate particular solutions ⋮ Order theory for discrete gradient methods

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Numerical solution of two-dimensional sine-Gordon and MBE models using Fourier spectral and high order explicit time stepping methods
• Energy-preserving integrators and the structure of B-series
• Numerical simulation of two-dimensional sine-Gordon solitons via a local weak meshless technique based on the radial point interpolation method (RPIM)
• A note on the efficient implementation of Hamiltonian BVMs
• Energy conservation issues in the numerical solution of the semilinear wave equation
• Symplectic Runge-Kutta and related methods: Recent results
• Two energy conserving numerical schemes for the sine-Gordon equation
• A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions
• Numerical study of \(2+1\) dimensional sine-Gordon solitons
• Local structure-preserving algorithms for partial differential equations
• Numerical solution of the sine-Gordon equation
• Finite element approximation to two-dimensional sine-Gordon solitons
• Invariant-conserving finite difference algorithms for the nonlinear Klein-Gordon equation
• Symplectic integration of Hamiltonian wave equations
• Backward error analysis for multi-symplectic integration methods
• Numerical simulation of two-dimensional sine-Gordon solitons via a split cosine scheme
• Multi-symplectic Runge-Kutta collocation methods for Hamiltonian wave equations
• Space-time spectral method for the two-dimensional generalized sine-Gordon equation
• The solution of the two-dimensional sine-Gordon equation using the method of lines
• Symplectic and multisymplectic Fourier pseudospectral discretizations for the Klein-Gordon equation
• Preserving energy resp. dissipation in numerical PDEs using the ``Average Vector Field method
• Efficient implementation of Gauss collocation and Hamiltonian boundary value methods
• A third order numerical scheme for the two-dimensional sine-Gordon equation
• High Order Multisymplectic Runge--Kutta Methods
• Hamiltonian Boundary Value Methods (Energy Conserving Discrete Line Integral Methods)
• Convergence of the interpolated coefficient finite element method for the two-dimensional elliptic sine-Gordon equations
• Simulating Hamiltonian Dynamics
• Symplectic Geometric Algorithms for Hamiltonian Systems
• Geometric integration using discrete gradients
• Backward Error Analysis for Numerical Integrators
• High Order Symplectic Schemes for the Sine-Gordon Equation^*
• Multisymplectic Geometry and Multisymplectic Scheme for the Nonlinear Klein Gordon Equation
• Finite Difference Calculus Invariant Structure of a Class of Algorithms for the Nonlinear Klein–Gordon Equation
• A new class of energy-preserving numerical integration methods
• A modified explicit numerical scheme for the two-dimensional sine-Gordon equation
• Numerical methods for Hamiltonian PDEs
• Geometric Numerical Integration
• Multi-symplectic Fourier pseudospectral method for the nonlinear Schrödinger equation

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