Two classes of linearly implicit local energy-preserving approach for general multi-symplectic Hamiltonian PDEs
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Publication:2222678
DOI10.1016/j.jcp.2019.108975zbMath1453.65437OpenAlexW2978703516WikidataQ114163508 ScholiaQ114163508MaRDI QIDQ2222678
Publication date: 27 January 2021
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jcp.2019.108975
Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Numerical methods for Hamiltonian systems including symplectic integrators (65P10)
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Cites Work
- On symplectic and multisymplectic schemes for the KdV equation
- Symplectic and multisymplectic numerical methods for Maxwell's equations
- Some new structure-preserving algorithms for general multi-symplectic formulations of Hamiltonian PDEs
- Multi-symplectic integration of the Camassa-Holm equation
- Splitting multisymplectic integrators for Maxwell's equations
- Numerical study of \(2+1\) dimensional sine-Gordon solitons
- Explicit multi-symplectic methods for Klein-Gordon-Schrödinger equations
- Local structure-preserving algorithms for partial differential equations
- Hamiltonian-conserving discrete canonical equations based on variational difference quotients
- On the stability of symplectic and energy-momentum algorithms for nonlinear Hamiltonian systems with symmetry
- Backward error analysis for multi-symplectic integration methods
- Multisymplectic box schemes and the Korteweg-de Vries equation.
- Linear, first and second-order, unconditionally energy stable numerical schemes for the phase field model of homopolymer blends
- The scalar auxiliary variable (SAV) approach for gradient flows
- Numerical simulation of two-dimensional sine-Gordon solitons via a split cosine scheme
- Symplectic wavelet collocation method for Hamiltonian wave equations
- Efficient linear schemes with unconditional energy stability for the phase field elastic bending energy model
- Decoupled local/global energy-preserving schemes for the \(N\)-coupled nonlinear Schrödinger equations
- Efficient local energy dissipation preserving algorithms for the Cahn-Hilliard equation
- A linearly implicit and local energy-preserving scheme for the sine-Gordon equation based on the invariant energy quadratization approach
- Explicit multi-symplectic extended leap-frog methods for Hamiltonian wave equations
- Local energy-preserving and momentum-preserving algorithms for coupled nonlinear Schrödinger system
- A General Framework for Deriving Integral Preserving Numerical Methods for PDEs
- Simulating Hamiltonian Dynamics
- A new explicit multisymplectic scheme for the regularized long-wave equation
- Geometric integration using discrete gradients
- Multisymplectic geometry and multisymplectic Preissmann scheme for the KdV equation
- A robust, mass conservative scheme for two-phase flow in porous media including Hölder continuous nonlinearities
- Optimal error estimates of finite difference methods for the Gross-Pitaevskii equation with angular momentum rotation
- Efficient energy‐preserving scheme of the three‐coupled nonlinear Schrödinger equation
- A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows
- The Multisymplectic Diamond Scheme
- Local energy‐ and momentum‐preserving schemes for Klein‐Gordon‐Schrödinger equations and convergence analysis
- A new class of energy-preserving numerical integration methods
- Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity
- Multi-symplectic spectral discretizations for the Zakharov-Kuznetsov and shallow water equations
- Multi-symplectic Fourier pseudospectral method for the nonlinear Schrödinger equation
- Dissipative or conservative finite-difference schemes for complex-valued nonlinear partial differential equations
- Local structure-preserving algorithms for general multi-symplectic Hamiltonian PDEs