Numerical conservations of energy, momentum and actions in the full discretisation for nonlinear wave equations
DOI10.1007/s10915-023-02405-0OpenAlexW4388911484MaRDI QIDQ6184274
Yao-Lin Jiang, Unnamed Author, Zhen Miao
Publication date: 5 January 2024
Published in: Journal of Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10915-023-02405-0
Second-order nonlinear hyperbolic equations (35L70) Numerical methods for initial value problems involving ordinary differential equations (65L05) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Numerical methods for Hamiltonian systems including symplectic integrators (65P10)
Cites Work
- Unnamed Item
- Long-term analysis of the Störmer-Verlet method for Hamiltonian systems with a solution-dependent high frequency
- Explicit symplectic RKN methods for perturbed non-autonomous oscillators: splitting, extended and exponentially fitting methods
- Metastable energy strata in numerical discretizations of weakly nonlinear wave equations
- One-stage exponential integrators for nonlinear Schrödinger equations over long times
- Spectral semi-discretisations of weakly non-linear wave equations over long times
- Conservation of energy, momentum and actions in numerical discretizations of non-linear wave equations
- Birkhoff normal form for some nonlinear PDEs
- Symmetric and arbitrarily high-order Birkhoff-Hermite time integrators and their long-time behaviour for solving nonlinear Klein-Gordon equations
- Conservation of invariants by symmetric multistep cosine methods for second-order partial differential equations
- A long-term numerical energy-preserving analysis of symmetric and/or symplectic extended RKN integrators for efficiently solving highly oscillatory Hamiltonian systems
- Long-time analysis of nonlinearly perturbed wave equations via modulated Fourier expansions
- Conserved quantities of some Hamiltonian wave equations after full discretization
- Numerical energy conservation for multi-frequency oscillatory differential equations
- PLANE WAVE STABILITY OF THE SPLIT-STEP FOURIER METHOD FOR THE NONLINEAR SCHRÖDINGER EQUATION
- Long-term analysis of semilinear wave equations with slowly varying wave speed
- Multistep cosine methods for second-order partial differential systems
- Long-Time Energy Conservation of Numerical Methods for Oscillatory Differential Equations
- Closing the gap between trigonometric integrators and splitting methods for highly oscillatory differential equations
- Trigonometric integrators for quasilinear wave equations
- Structure-Preserving Algorithms for Oscillatory Differential Equations
- Error Estimates of Some Splitting Schemes for Charged-Particle Dynamics under Strong Magnetic Field
- Analysis of exponential splitting methods for inhomogeneous parabolic equations
- Error Analysis of Trigonometric Integrators for Semilinear Wave Equations
- Modified Trigonometric Integrators
- Modulated Fourier expansions and heterogeneous multiscale methods
- Geometric Numerical Integration
- Arbitrary-order trigonometric Fourier collocation methods for multi-frequency oscillatory systems
- Geometric Two-Scale Integrators for Highly Oscillatory System: Uniform Accuracy and Near Conservations
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